Richard, Jean-Pierre Time-delay systems: an overview of some recent advances and open problems. (English) Zbl 1145.93302 Automatica 39, No. 10, 1667-1694 (2003). Summary: After presenting some motivations for the study of time-delay system, this paper recalls modifications (models, stability, structure) arising from the presence of the delay phenomenon. A brief overview of some control approaches is then provided, the sliding mode and time-delay controls in particular. Lastly, some open problems are discussed: the constructive use of the delayed inputs, the digital implementation of distributed delays, the control via the delay, and the handling of information related to the delay value. Cited in 798 Documents MSC: 93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory 93C23 Control/observation systems governed by functional-differential equations 93B12 Variable structure systems 34K20 Stability theory of functional-differential equations Keywords:Delay systems; Aftereffect; Dead-time; Functional differential equations × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Abdallah, C., Birdwell, J. D., Chiasson, J., Chupryna, V., Tang, Z., & Wang, T. (2001). Load balancing instabilities due to time delays in parallel computations. In Third IFAC workshop on time delay systems; Abdallah, C., Birdwell, J. D., Chiasson, J., Chupryna, V., Tang, Z., & Wang, T. (2001). Load balancing instabilities due to time delays in parallel computations. In Third IFAC workshop on time delay systems · Zbl 1089.68562 [2] Abdallah, C., & Chiasson, J. (2001). Stability of communication networks in the presence of delays. In Third IFAC workshop on time delay systems; Abdallah, C., & Chiasson, J. (2001). Stability of communication networks in the presence of delays. In Third IFAC workshop on time delay systems [3] Abdallah, G., Dorato, P., Benitez-Read, J., & Byrne, R. (1993). Delayed positive feedback can stabilize oscillatory systems. In ACC’93American control conference; Abdallah, G., Dorato, P., Benitez-Read, J., & Byrne, R. (1993). Delayed positive feedback can stabilize oscillatory systems. In ACC’93American control conference [4] Aernouts, W.; Roose, D.; Sepulchre, R., Delayed control of a Moore-Greitzer axial compressor model, International Journal of Bifurcation and Chaos, 10, 2, 1157-1164 (2000) [5] Aggoune, W. (1999). Contribution à la Stabilisation de Systèmes Non Linéaires: Application aux Systèmes Non Réguliers et aux Systèmes à Retards; Aggoune, W. (1999). Contribution à la Stabilisation de Systèmes Non Linéaires: Application aux Systèmes Non Réguliers et aux Systèmes à Retards [6] Ailon, A.; Gil, M. I., Stability analysis of a rigid robot with output-based controller and time-delay, Systems and Control Letters, 40, 1, 31-35 (2000) · Zbl 0977.93056 [7] Akian, M., Bliman, P. A., & Sorine, M. (1998). P.I. control of nonlinear oscillations for a system with delay; Akian, M., Bliman, P. A., & Sorine, M. (1998). P.I. control of nonlinear oscillations for a system with delay · Zbl 1008.93049 [8] Al-Amer, S. H., & Al-Sunni, F. M. (2000). Approximation of time-delay systems. In ACC’00American control conference; Al-Amer, S. H., & Al-Sunni, F. M. (2000). Approximation of time-delay systems. In ACC’00American control conference [9] Artstein, Z., Linear systems with delayed controlsA reduction, IEEE Transactions on Automatic Control, 27, 4, 869-879 (1982) · Zbl 0486.93011 [10] Åström, K. J.; Hang, C. C.; Lim, B. C., A new Smith predictor for controlling a process with an integrator and long deadtime, IEEE Transactions on Automatic Control, 39, 2, 343-345 (1994) · Zbl 0800.93163 [11] Banks, H. T.; Kappel, F., Spline approximations for functional differential equations, Journal of Differential Equations, 34, 496-522 (1979) · Zbl 0422.34074 [12] Banks, S. P., Nonlinear delay systems, Lie algebras and Lyapunov transformations, IMA Journal of Mathematical Control and Information, 19, 1-2, 59-72 (2002) · Zbl 1112.93328 [13] Bartholoméüs, A.; Dambrine, M.; Richard, J. P., Bounded domains and constrained control of linear time-delays systems, JESA, European Journal of Automatic Systems, 31, 6, 1001-1014 (1997) [14] Battle, C.; Miralles, A., On the approximation of delay elements by feedback, Automatica, 36, 659-664 (2000) · Zbl 0973.93019 [15] Beghi, A.; Lepschy, A.; Viaro, U., Approximating delay elements by feedback, IEEE Transactions on Circuits and Systems, 44, 824-828 (1997) [16] Belkoura, L., Dambrine, M., Richard, J.-P., & Orlov, Y. (1998). Sliding mode on-line identification of delay systems. In VSS’98, Fifth international workshop on variable structure systems; Belkoura, L., Dambrine, M., Richard, J.-P., & Orlov, Y. (1998). Sliding mode on-line identification of delay systems. In VSS’98, Fifth international workshop on variable structure systems [17] Belkoura, L., Richard, J. P., & Orlov, Y. (2000). Identifiability of linear time delay systems. In Second IFAC workshop on linear time delay systems; Belkoura, L., Richard, J. P., & Orlov, Y. (2000). Identifiability of linear time delay systems. In Second IFAC workshop on linear time delay systems [18] Bellen, A., & Zennaro, M. (2001). A free step-size implementation of second order stable methods for neutral delay differential equations. In Third IFAC workshop on time delay systems; Bellen, A., & Zennaro, M. (2001). A free step-size implementation of second order stable methods for neutral delay differential equations. In Third IFAC workshop on time delay systems [19] Bellman, R.; Cooke, K. L., Differential difference equations (1963), Academic Press: Academic Press New York · Zbl 0115.30102 [20] Bellman, R.; Cooke, K. L., On the computational solution of a class of functional differential equations, Journal of Mathematical Analysis and Applications, 12, 495-500 (1965) · Zbl 0138.32103 [21] Biberovic, E., Iftar, A., & Ozbay, H. (2001). A solution to the robust flow control problem for networks with multiple bottlenecks. In 40th IEEE CDC’01Conference on decision and control; Biberovic, E., Iftar, A., & Ozbay, H. (2001). A solution to the robust flow control problem for networks with multiple bottlenecks. In 40th IEEE CDC’01Conference on decision and control [22] Blanchini, F.; Ryan, E. P., A Razumikhin-type lemma for functional differential equations with application to adaptive control, Automatica, 35, 5, 809-818 (1999) · Zbl 0934.93038 [23] Bonnet, C.; Partington, J. R., Stabilization of fractional exponential systems including delays, Kybernetika, 37, 3, 345-354 (2001) · Zbl 1265.93211 [24] Bonnet, C.; Partington, J. R.; Sorine, M., Robust control and tracking of a delay system with discontinuous nonlinearity in the feedback, International Journal of Control, 72, 15, 1354-1364 (1999) · Zbl 0960.93042 [25] Bonnet, C.; Partington, J. R.; Sorine, M., Robust stabilization of a delay system with saturating actuator or sensor, International Journal of Robust and Nonlinear Control, 10, 579-590 (2000) · Zbl 0973.93045 [26] Borne, P., Dambrine, M., Perruquetti, W., & Richard, J. P. (2002). Vector Lyapunov functions: Nonlinear, time-varying, ordinary and functional differential equations. Stability and control: Theory, methods and applications; Borne, P., Dambrine, M., Perruquetti, W., & Richard, J. P. (2002). Vector Lyapunov functions: Nonlinear, time-varying, ordinary and functional differential equations. Stability and control: Theory, methods and applications · Zbl 1039.34066 [27] Boukas, E. K., & Liu, Z. K. (2002). Deterministic and stochastic time-delay systems. Control engineering; Boukas, E. K., & Liu, Z. K. (2002). Deterministic and stochastic time-delay systems. Control engineering · Zbl 1056.93001 [28] Brethé, D. (1997). Contribution à l’Etude de la Stabilisation des Systèmes Linéaires à Retards; Brethé, D. (1997). Contribution à l’Etude de la Stabilisation des Systèmes Linéaires à Retards [29] Bushnell, L., Editorial: Networks and control, IEEE Control System Magazine, 21, 1, 22-99 (2001), (special section on networks and control) [30] Byrnes, C. I.; Spong, M. W.; Tarn, T. J., A several complex variables approach to feedback stabilization of linear neutral delay-differential systems, Mathematical Systems Theory, 17, 97-133 (1984) · Zbl 0539.93064 [31] Cao, Y. Y.; Lam, J., \(H_∞\) control of uncertain markovian jump systems with time delay, IEEE Transactions on Automatic Control, 45, 1, 77-83 (2000) · Zbl 0983.93075 [32] Chang, P. H.; Lee, J. W.; Park, S. H., Time delay observerA robust observer for nonlinear plants, ASME Journal of Dynamic Systems Measurement and Control, 119, 521-527 (1997) · Zbl 0900.93047 [33] Chang, P. H., & Park, S. H. (1998). The enhanced time delay observer for nonlinear systems. In 37th IEEE CDC’98Conference on decision and control; Chang, P. H., & Park, S. H. (1998). The enhanced time delay observer for nonlinear systems. In 37th IEEE CDC’98Conference on decision and control [34] Chen, J.; Latchman, H. A., Frequency sweeping tests for stability independent of delay, IEEE Transactions on Automatic Control, 40, 9, 1640-1645 (1995) · Zbl 0834.93044 [35] Cheres, E.; Gutman, S.; Palmor, Z. J., Stabilization of uncertain dynamic systems including state delay, IEEE Transactions on Automatic Control, 34, 11, 1199-1203 (1989) · Zbl 0693.93059 [36] Choi, H. H. (1999). An LMI approach to sliding mode control design for a class of uncertain time delay systems. In ECC’99Fifth European control conference; Choi, H. H. (1999). An LMI approach to sliding mode control design for a class of uncertain time delay systems. In ECC’99Fifth European control conference [37] Choi, H. H.; Chung, M. J., Memoryless \(H_∞\) controller design for linear systems with delayed state and control, Automatica, 31, 6, 917-919 (1995) · Zbl 0829.93021 [38] Choi, H. H.; Chung, M. J., Observer-based \(H_∞\) controller design for state delayed linear systems, Automatica, 32, 7, 1073-1075 (1996) · Zbl 0850.93215 [39] Choi, H. H.; Chung, M. J., Robust observer-based \(H_∞\) controller design for linear uncertain time-delay systems, Automatica, 33, 9, 1749-1752 (1997) · Zbl 1422.93062 [40] Choi, S. B.; Hedrick, J. K., An observer-based controller design method for improving air/fuel characterization of spark ignition engines, IEEE Transactions on Control Systems Technology, 6, 3, 325-334 (1998) [41] Conte, G.; Perdon, A. M., The disturbance decoupling problem for systems over a ring, SIAM Journal on Control and Optimization, 33, 3, 750-764 (1995) · Zbl 0831.93011 [42] Conte, G.; Perdon, A. M., Non-interacting control problems for delay-differential systems via systems over rings, JESA, European Journal on Automatic Systems, 31, 6, 1059-1076 (1997) [43] Conte, G., & Perdon, A. M. (1998). Systems over rings: Theory and applications. In First IFAC workshop on linear time delay systemsPlenary lecture; Conte, G., & Perdon, A. M. (1998). Systems over rings: Theory and applications. In First IFAC workshop on linear time delay systemsPlenary lecture [44] Dambrine, M., Gouaisbaut, F., Perruquetti, W., & Richard, J.-P. (1998). Robustness of sliding mode control under delays effects: A case study. In CESA’98IEEE-IMACS conference on computer engineering in system applications; Dambrine, M., Gouaisbaut, F., Perruquetti, W., & Richard, J.-P. (1998). Robustness of sliding mode control under delays effects: A case study. In CESA’98IEEE-IMACS conference on computer engineering in system applications [45] Dambrine, M.; Richard, J. P.; Borne, P., Feedback control of time-delay systems with bounded control and state, Mathematical Problems in Engineering, 1, 77-87 (1995) · Zbl 0918.93040 [46] Darouach, M., Linear functional observers for systems with delays in state variables, IEEE Transactions on Automatic Control, 46, 3, 491-496 (2001) · Zbl 1056.93503 [47] Darouach, M.; Pierrot, P.; Richard, E., Design of reduced-order observers without internal delays, IEEE Transactions on Automatic Control, 44, 9, 1711-1713 (1999) · Zbl 0958.93015 [48] Datko, R., A paradigm of ill-posedness with respect to time delays, IEEE Transactions on Automatic Control, 43, 7, 964-967 (1998) · Zbl 0968.93067 [49] De Santis, A.; Germani, A.; Jetto, L., Approximation of the algebraic Riccati equation in the Hilbert space of Hilbert-Schmidt operators, SIAM Journal on Control and Optimization, 4, 847-874 (1993) · Zbl 0785.93049 [50] Delfour, M.; Mitter, S., Controllability, observability and optimal feedback control of affine, hereditary, differential systems, SIAM Journal on Control and Optimization, 10, 298-328 (1972) · Zbl 0242.93011 [51] DeSouza, C. E., Palhares, R. E., & Peres, P. L. D. (1999). Robust \(H_∞\)38th IEEE CDC’99Conference on decision and control; DeSouza, C. E., Palhares, R. E., & Peres, P. L. D. (1999). Robust \(H_∞\)38th IEEE CDC’99Conference on decision and control [52] Dieulot, J. Y., & Richard, J. P. (2001). Tracking control of a nonlinear system with input-dependent delay. In 40th IEEE CDC’01Conference on decision and control; Dieulot, J. Y., & Richard, J. P. (2001). Tracking control of a nonlinear system with input-dependent delay. In 40th IEEE CDC’01Conference on decision and control [53] Dion, J. M., Dugard, L., & Niculescu, S. I. (2001). Time delay systems. Kybernetica37; Dion, J. M., Dugard, L., & Niculescu, S. I. (2001). Time delay systems. Kybernetica37 · Zbl 1265.93197 [54] Diop, S.; Kolmanovsky, I.; Moraal, P.; vanNieuwstadt, M., Preserving stability/performance when facing an unknown time delay, Control Engineering Practice, 9, 1319-1325 (2001) [55] Dugard, L.; Verriest, E. I., Stability and control of time-delay systems, Lecture notes in control and information sciences, Vol. 228 (1997), Springer: Springer Berlin [56] Dym, H.; Georgiou, T. T.; Smith, M. C., Explicit formulas for optimally robust controllers for delay systems, IEEE Transactions on Automatic Control, 40, 4, 656-669 (1995) · Zbl 0830.93027 [57] El-Khazaly, R., Variable structure robust control of uncertain time-delay systems, Automatica, 34, 3, 327-332 (1998) · Zbl 0965.93025 [58] Elsgolts, L. E.; Norkin, S. B., Introduction to the theory and application of differential equations with deviating arguments, Mathematics in science and engineering, Vol. 105 (1973), Academic Press: Academic Press New York · Zbl 0287.34073 [59] Engelborghs, K.; Dambrine, M.; Roose, D., Limitations of a class of stabilization methods for delay systems, IEEE Transactions on Automatic Control, 46, 2, 336-339 (2001) · Zbl 1056.93607 [60] Fairmar, F. W.; Kumar, A., Delay-less observers for systems with delay, IEEE Transactions on Automatic Control, 31, 3, 258-259 (1986) · Zbl 0597.93010 [61] Fattouh, A., Sename, O., & Dion, J. M. (2000). A LMI approach to robust observer design for linear time-delay systems. In 39th IEEE CDC’00Conference on decision and control; Fattouh, A., Sename, O., & Dion, J. M. (2000). A LMI approach to robust observer design for linear time-delay systems. In 39th IEEE CDC’00Conference on decision and control · Zbl 1274.93079 [62] Fiagbedzi, Y. A.; Pearson, A. E., Feedback stabilization of linear autonomous time lag systems, IEEE Transactions on Automatic Control, 31, 847-855 (1986) · Zbl 0601.93045 [63] Fliess, M., Marquez, R., & Mounier, H. (2001). PID-like regulators for a class of linear delay systems. In ECC’01Sixth European control conference; Fliess, M., Marquez, R., & Mounier, H. (2001). PID-like regulators for a class of linear delay systems. In ECC’01Sixth European control conference · Zbl 1021.93015 [64] Fliess, M., & Mounier, H. (1995). Interpretation and comparison of various types of delay system controllabilities. In IFAC conference on system structure and control; Fliess, M., & Mounier, H. (1995). Interpretation and comparison of various types of delay system controllabilities. In IFAC conference on system structure and control [65] Foda, S. G.; Mahmoud, M. S., Adaptive stabilization of delay differential systems with unknown uncertainty bounds, International Journal on Control, 71, 2, 259-275 (1998) · Zbl 0965.93093 [66] Foias, C.; Özbay, H.; Tannenbaum, A., Robust control of infinite dimensional systems: A frequency domain method, Lecture notes in control and information sciences, Vol. 209 (1996), Springer: Springer Berlin · Zbl 0839.93003 [67] Fridman, E., New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems, System and Control Letters, 43, 4, 309-319 (2001) · Zbl 0974.93028 [68] Fridman, E.; Fridman, L. M.; Shustin, E. I., Steady modes in a discontinuous control system with time delay and periodic disturbances, ASME Journal of Dynamic Systems, Measurements and Control, 122, 4, 732-737 (2000) [69] Fridman, E.; Shaked, U., A descriptor system approach to \(H_∞\) control of linear time-delay systems, IEEE Transactions on Automatic Control, 47, 2, 253-270 (2002) · Zbl 1364.93209 [70] Fridman, E., & Shaked, U. (2003). Delay systems. International Journal of Robust and Nonlinear Control13; Fridman, E., & Shaked, U. (2003). Delay systems. International Journal of Robust and Nonlinear Control13 · Zbl 1364.93591 [71] Fridman, L. M., Fridman, E., & Shustin, E. I. (1996). Steady modes and sliding modes in the relay control systems with time delay. In 35th IEEE CDC’96Conference on decision and control; Fridman, L. M., Fridman, E., & Shustin, E. I. (1996). Steady modes and sliding modes in the relay control systems with time delay. In 35th IEEE CDC’96Conference on decision and control [72] Fu, M., Li, H., & Niculescu, S. I. (1997). Robust stability and stabilization of time-delay systems via integral quadratic constraint approachLecture notes in control and information sciences; Fu, M., Li, H., & Niculescu, S. I. (1997). Robust stability and stabilization of time-delay systems via integral quadratic constraint approachLecture notes in control and information sciences · Zbl 0916.93068 [73] Gao, J.; Huang, B.; Wang, Z., LMI-based robust \(H_∞\) control of uncertain linear jump systems with time-delays, Automatica, 37, 1141-1146 (2001) · Zbl 0989.93029 [74] Ge, J. H.; Frank, P. M.; Lin, C. F., Robust \(H_∞\) state feedback control for linear systems with state delay and parameter uncertainty, Automatica, 32, 8, 1183-1185 (1996) · Zbl 0850.93216 [75] Georgiou, T. T.; Smith, M. C., Robust stabilization in the gap metricController design for distributed plants, IEEE Transactions on Automatic Control, 37, 1133-1143 (1992) · Zbl 0764.93033 [76] Georgiou, T. T.; Smith, M. C., Robustness analysis of nonlinear feedback systemsAn input-output approach, IEEE Transactions on Automatic Control, 42, 9, 1200-1221 (1997) · Zbl 0889.93043 [77] Georgiou, T. T.; Smith, M. C., Bézout factors and \(l^1\)-optimal controllers for delay systems using a two-parameter compensator scheme, IEEE Transactions on Automatic Control, 44, 8, 1512-1521 (1999) · Zbl 0959.93052 [78] Germani, A., Manes, C., & Pepe, P. (1996). Linearization of input-output mapping for nonlinear delay systems via static state feedback. In CESA’96IEEE-IMACS conference on computer engineering in system applications; Germani, A., Manes, C., & Pepe, P. (1996). Linearization of input-output mapping for nonlinear delay systems via static state feedback. In CESA’96IEEE-IMACS conference on computer engineering in system applications [79] Germani, A., Manes, C., & Pepe, P. (1998). A state observer for nonlinear delay systems. In 37th IEEE CDC’98Conference on decision and control; Germani, A., Manes, C., & Pepe, P. (1998). A state observer for nonlinear delay systems. In 37th IEEE CDC’98Conference on decision and control [80] Gibson, J. S., Linear quadratic optimal control of hereditary differential systemsInfinite-dimensional Riccati equations and numerical approximation, SIAM Journal on Control and Optimization, 31, 95-139 (1983) · Zbl 0557.49017 [81] Glader, C.; Hognas, G.; Mäkilä, P. M.; Toivonen, H. T., Approximation of delay systemsA case study, International Journal of Control, 53, 2, 369-390 (1991) · Zbl 0745.93016 [82] Glielmo, L., Santini, S., & Cascella, I. (2000). Stability of linear time-delay systems: A delay-dependent criterion with a tight conservatism bound. In ACC’00American control conference; Glielmo, L., Santini, S., & Cascella, I. (2000). Stability of linear time-delay systems: A delay-dependent criterion with a tight conservatism bound. In ACC’00American control conference [83] Glover, K.; Lam, J.; Partington, J. R., Rational approximation of a class of infinite dimensional system ISingular value of Hankel operator, Mathematics of Control Circulation and Systems, 3, 325-344 (1990) · Zbl 0727.41020 [84] Glover, K., & Partington, J. R. (1987). Bounds on the achievable accuracy in model reduction; Glover, K., & Partington, J. R. (1987). Bounds on the achievable accuracy in model reduction [85] Glüsing-Lüerßen, H., A behavioral approach to delay-differential systems, SIAM Journal on Control and Optimization, 35, 2, 480-499 (1997) · Zbl 0876.93022 [86] Glüsing-Lüerßen, H. (1997b). Realization behaviors given by delay-differential equations. In ECC’97Fourth European control conference; Glüsing-Lüerßen, H. (1997b). Realization behaviors given by delay-differential equations. In ECC’97Fourth European control conference [87] Gorecki, H.; Fuksa, S.; Grabowski, P.; Korytowski, A., Analysis and synthesis of time delay systems (1989), Wiley: Wiley New York · Zbl 0695.93002 [88] Gouaisbaut, F.; Dambrine, M.; Richard, J. P., Robust control of systems with variable delayA sliding mode control design via LMIs, System and Control Letters, 46, 4, 219-230 (2002) · Zbl 0994.93004 [89] Gouaisbaut, F., Perruquetti, W., Orlov, Y., & Richard, J. P. (1999a). A sliding-mode controller for linear time-delay systems. In ECC’99Fifth European control conference; Gouaisbaut, F., Perruquetti, W., Orlov, Y., & Richard, J. P. (1999a). A sliding-mode controller for linear time-delay systems. In ECC’99Fifth European control conference [90] Gouaisbaut, F., Perruquetti, W., & Richard, J. P. (1999b). A sliding-mode control for linear systems with input and state delays. In 38th IEEE CDC’99Conference on decision and control; Gouaisbaut, F., Perruquetti, W., & Richard, J. P. (1999b). A sliding-mode control for linear systems with input and state delays. In 38th IEEE CDC’99Conference on decision and control [91] Goubet, A., Dambrine, M., & Richard, J. P. (1995). An extension of stability criteria for linear and nonlinear time delay systems. In IFAC conference on system structure and control; Goubet, A., Dambrine, M., & Richard, J. P. (1995). An extension of stability criteria for linear and nonlinear time delay systems. In IFAC conference on system structure and control [92] Goubet-Bartholomeus, A.; Dambrine, M.; Richard, J. P., Stability of perturbed systems with time-varying delay, Systems and Control Letters, 31, 155-163 (1997) · Zbl 0901.93047 [93] Gu, K., A generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time-delay systems, International Journal on Robust and Nonlinear Control, 9, 1-14 (1999) · Zbl 0923.93046 [94] Gu, G.; Khargonekar, P. P.; Lee, E. B., Approximation of infinite-dimensional systems, IEEE Transactions on Automatic Control, 34, 6, 832-852 (1992) [95] Gu, K., Discretization schemes for Lyapunov-Krasovskii functionals in time delay systems, Kybernetica, 37, 4, 479-504 (2001) · Zbl 1265.93176 [96] Gu, K., & Niculescu, S. I. (1999). Additional dynamics in transformed time-delay systems. In 38th IEEE CDC99Conference on decision and control; Gu, K., & Niculescu, S. I. (1999). Additional dynamics in transformed time-delay systems. In 38th IEEE CDC99Conference on decision and control [97] Gu, K.; Niculescu, S. I., Further remarks on additional dynamics in various model transformations of linear delay systems, IEEE Transactions on Automatic Control, 46, 3, 497-500 (2001) · Zbl 1056.93511 [98] Hale, J. K.; Verduyn-Lunel, S., Strong stabilization of neutral functional differential equations, IMA Journal of Mathematical Control Information, 19, 1-2, 5-24 (2002) · Zbl 1005.93026 [99] Hale, J. K.; Verduyn-Lunel, S. M., Introduction to functional differential equations, Applied Mathematical Sciences, Vol. 99 (1993), Springer: Springer New York · Zbl 0787.34002 [100] Hennet, J.-C.; Tarbouriech, S., Stability conditions of constrained delay systems via positive invariance, International Journal of Robust and Nonlinear Control, 8, 3, 265-278 (1998) · Zbl 0914.93048 [101] Hirai, K.; Satoh, Y., Stability of a system with variable time-delay, IEEE Transactions on Automatic Control, 25, 3, 552-554 (1980) · Zbl 0429.93040 [102] Hotzel, R.; Fliess, M., On linear systems with a fractional derivationIntroductory theory and examples, Mathematics and Computers in Simulation, 45, 3-4, 385-395 (1998) · Zbl 1017.93508 [103] Hsia, T. C., & Gao, L. S. (1990). Robot manipulator control using decentralized time-invariant time-delayed controller. In IEEE international conference on robotics and automation; Hsia, T. C., & Gao, L. S. (1990). Robot manipulator control using decentralized time-invariant time-delayed controller. In IEEE international conference on robotics and automation [104] Huang, W., Generalization of Lyapunov’s theorem in a linear delay system, Journal of Mathematical Analysis and Applications, 142, 83-94 (1989) · Zbl 0705.34084 [105] Huang, Y. P.; Zhou, K., Robust stability of uncertain time delay systems, IEEE Transactions on Automatic Control, 45, 11, 2169-2173 (2000) · Zbl 0989.93066 [106] Infante, E. F.; Castelan, W. B., A Lyapunov functional for a matrix difference-differential equation, Journal of Differential Equations, 29, 439-451 (1978) · Zbl 0354.34049 [107] Ionescu, V.; Niculescu, S. I.; Dion, J. M.; Dugard, L.; Li, H., Generalized Popov theory applied to state-delayed systems, Automatica, 37, 1, 91-97 (2001) · Zbl 0965.93083 [108] Ionescu, V.; Oara, C.; Weiss, M., Generalized Riccati theory (1998), Wiley: Wiley New York [109] Ivanov, A. F., & Losson, J. (1995). Stable rapidly oscillating solutions in delay equations with negative feedback; Ivanov, A. F., & Losson, J. (1995). Stable rapidly oscillating solutions in delay equations with negative feedback · Zbl 1015.34054 [110] Izmailov, R., Analysis and optimization of feedback control algorithms for data transfers in high-speed networks, SIAM Journal of Control and Optimization, 34, 1767-1780 (1996) · Zbl 0861.90055 [111] Jalili, N., & Olgac, N. (1998). Optimum delayed feedback vibration absorber for MDOF mechanical structure. In 37th IEEE CDC98Conference on decision and control; Jalili, N., & Olgac, N. (1998). Optimum delayed feedback vibration absorber for MDOF mechanical structure. In 37th IEEE CDC98Conference on decision and control [112] Jankovic, M., Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems, IEEE Transactions on Automatic Control, 46, 7, 1048-1060 (2001) · Zbl 1023.93056 [113] Jeong, H. S.; Lee, C. W., Time delay control with state feedback for azimuth motion of the frictionless positioning device, IEEE-ASME Transactions on Mechatronics, 2, 3, 161-168 (1997) [114] Jun, M., & Safonov, M. G. (2000). Stability analysis of a system with time-delayed states. In ACC00American control conference; Jun, M., & Safonov, M. G. (2000). Stability analysis of a system with time-delayed states. In ACC00American control conference [115] Karrakchou, J., & Rabah, R. (1996). Quelques éléments sur la controlabilité des systèmes en dimension infinie. In CNRS conf. analyse et commande des systèmes avec retards; Karrakchou, J., & Rabah, R. (1996). Quelques éléments sur la controlabilité des systèmes en dimension infinie. In CNRS conf. analyse et commande des systèmes avec retards [116] Kato, J., On Liapunov-Razumikhin type theorems for functional differential equations, The Mathematical Society of Japan, Kobe, Funkcialaj Ekvacioj, 16, 3, 225-239 (1973) · Zbl 0321.34056 [117] Katz, I. I. (1998). Liapunov Method in Stability of Stochastic Systems; Katz, I. I. (1998). Liapunov Method in Stability of Stochastic Systems [118] Khan, B. Z.; Lehman, B., Setpoint PI controllers for systems with large normalized dead time, IEEE Transactions on Control Systems Technology, 4, 4, 459-466 (1996) [119] Kharitonov, V. (1998). Robust stability analysis of time delay systems: A survey. In Fourth IFAC conference on system structure and controlPenary lecture; Kharitonov, V. (1998). Robust stability analysis of time delay systems: A survey. In Fourth IFAC conference on system structure and controlPenary lecture [120] Kharitonov, V. L.; Melchior-Aguliar, D., On delay-dependent stability conditions, System and Control Letters, 40, 1, 71-76 (2000) · Zbl 0977.93072 [121] Kharitonov, V. L., & Zhabko, A. P. (2001). Lyapunov-Krasovski approach to robust stability of time delay systems. In First IFAC/IEEE symposium on system structure and control; Kharitonov, V. L., & Zhabko, A. P. (2001). Lyapunov-Krasovski approach to robust stability of time delay systems. In First IFAC/IEEE symposium on system structure and control · Zbl 1014.93031 [122] Kim, W. S.; Hannaford, B.; Bejczy, A. K., Force-reflection and shared compliant control in operating telemanipulators with time-delay, IEEE Transactions on Robotics and Automation, 8, 2, 176-185 (1992) [123] Kojima, A.; Uchida, K.; Shimemura, E.; Ishijima, S., Robust stabilization of a system with delays in control, IEEE Transactions on Automatic Control, 39, 8, 1694-1698 (1994) · Zbl 0800.93985 [124] Kolmanovskii, V. B., Stability of some nonlinear functional differential equations, Journal of Nonlinear Differential Equations, 2, 185-198 (1995) · Zbl 0824.34081 [125] Kolmanovskii, V. B.; Maizenberg, T. L.; Richard, J. P., Mean square stability of difference equations with a stochastic delay, Nonlinear Analysis, 52, 3, 795-804 (2003) · Zbl 1029.39005 [126] Kolmanovskii, V. B.; Myshkis, A., Applied theory of functional differential equations, Mathematics and Applications, Vol. 85 (1992), Kluwer Academy: Kluwer Academy Dordrecht · Zbl 0785.34005 [127] Kolmanovskii, V. B.; Myshkis, A., Introduction to the theory and applications of functional differential equations (1999), Kluwer Academy: Kluwer Academy Dordrecht · Zbl 0917.34001 [128] Kolmanovskii, V. B., Niculescu, S. I., & Gu, K. (1999a). Delay effects on stability: A survey. In 38th IEEE CDC99Conference on decision and control; Kolmanovskii, V. B., Niculescu, S. I., & Gu, K. (1999a). Delay effects on stability: A survey. In 38th IEEE CDC99Conference on decision and control [129] Kolmanovskii, V. B.; Niculescu, S. I.; Richard, J. P., On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems, International Journal on Control, 72, 4, 374-384 (1999) · Zbl 0952.34057 [130] Kolmanovskii, V. B.; Nosov, V. R., Stability of functional differential equations (1986), Academic Press: Academic Press London · Zbl 0593.34070 [131] Kolmanovskii, V. B.; Richard, J. P., Stability of some linear systems with delay, IEEE Transactions on Automatic Control, 44, 5, 984-989 (1999) · Zbl 0964.34065 [132] Kolmanovskii, V. B.; Shaikhet, L. E., Control of systems with aftereffect, Transaction of Mathematical monographs, Vol. 157 (1996), American Mathematical Society: American Mathematical Society Providence, RI · Zbl 0937.93001 [133] Kolmanovskii, V. B., Tchangani, P. A., & Richard, J. P. (1998). Stability of linear systems with discrete-plus-distributed delay: Application of some model transformations. In MTNS9813th symposium on mathematical theory of networks and systems; Kolmanovskii, V. B., Tchangani, P. A., & Richard, J. P. (1998). Stability of linear systems with discrete-plus-distributed delay: Application of some model transformations. In MTNS9813th symposium on mathematical theory of networks and systems [134] Krasovskii, N. N. (1963). Stability of motion; Krasovskii, N. N. (1963). Stability of motion · Zbl 0109.06001 [135] Krtolica, R.; Özguner, Ü.; Chan, H.; Göktas, H.; Winkelman, J.; Liubakka, M., Stability of linear feedback systems with random communication delays, International Journal of Control, 59, 4, 925-953 (1991) · Zbl 0812.93073 [136] Kwon, H. W.; Pearson, A. E., Feedback stabilization of linear systems with delayed control, IEEE Transactions on Automatic Control, 25, 2, 266-269 (1980) · Zbl 0438.93055 [137] Lafay, J. F., Fliess, M., Mounier, H., & Sename, O. (1996). Sur la commandabilité des systèmes linéaires à retards. In CNRS conference analysis and control of systems with delays; Lafay, J. F., Fliess, M., Mounier, H., & Sename, O. (1996). Sur la commandabilité des systèmes linéaires à retards. In CNRS conference analysis and control of systems with delays [138] Lakshmikantham, V., & Leela, S. (1969). Differential and integral inequalities; Lakshmikantham, V., & Leela, S. (1969). Differential and integral inequalities · Zbl 0177.12403 [139] Lee, J. H., Moon, Y. S., & Kwon, W. H. (1996). Robust \(H_∞\)35th IEEE CDC96Conference on decision and control; Lee, J. H., Moon, Y. S., & Kwon, W. H. (1996). Robust \(H_∞\)35th IEEE CDC96Conference on decision and control [140] Lehman, B., The influence of delays when averaging slow and fast oscillating systemsOverview, IMA Journal of Mathematical Control Information, 19, 1-2, 201-216 (2002) · Zbl 1011.34001 [141] Lehman, B., & Weibel, S. P. (1998). Averaging theory for functional differential equations. In 37th IEEE CDC98Conference on decision and control; Lehman, B., & Weibel, S. P. (1998). Averaging theory for functional differential equations. In 37th IEEE CDC98Conference on decision and control [142] Lelevé, A., Fraisse, P., & Dauchez, P. (2001). Telerobotics over IP networks: Towards a low level real time architecture. In IROS01International conference on intelligent robots and systems; Lelevé, A., Fraisse, P., & Dauchez, P. (2001). Telerobotics over IP networks: Towards a low level real time architecture. In IROS01International conference on intelligent robots and systems [143] Lewis, R. M., Control-delayed system properties via an ordinary model, International Journal of Control, 30, 3, 477-490 (1979) · Zbl 0411.93026 [144] Leyva-Ramos, J.; Pearson, A. E., An asymptotic modal observer for linear autonomous time lag systems, IEEE Transactions on Automatic Control, 40, 1291-1294 (1995) · Zbl 0825.93084 [145] Li, X., & De Souza, C. E. (1996). Robust stabilization and \(H_∞\)Proceedings of 13th IFAC world congress; Li, X., & De Souza, C. E. (1996). Robust stabilization and \(H_∞\)Proceedings of 13th IFAC world congress [146] Loiseau, J. J. (1994). A 2-D transfert without minimal realization. In Sprann94IMACS; Loiseau, J. J. (1994). A 2-D transfert without minimal realization. In Sprann94IMACS [147] Loiseau, J. J. (1998). Algebraic tools for the control and stabilization of time-delay systems. In First IFAC workshop on linear time delay systemsPlenary lecture; Loiseau, J. J. (1998). Algebraic tools for the control and stabilization of time-delay systems. In First IFAC workshop on linear time delay systemsPlenary lecture [148] Loiseau, J. J., Invariant factors assignment for a class of time-delay systems, Kybernetika, 37, 3, 265-276 (2001) · Zbl 1265.93062 [149] Loiseau, J. J.; Brethé, D., 2-D exact model matching with stability, the structural approach, Bulletin of the Polish Academy of Science—Technical Sciences, 45, 2, 309-317 (1997) · Zbl 0895.93005 [150] Loiseau, J. J.; Brethé, D., The use of 2-D systems theory for the control of time-delay systems, JESA, European Journal of Automatic Systems, 31, 6, 1043-1058 (1997) [151] Loiseau, J. J.; Brethé, D., An effective algorithm for finite spectrum assignment of single-input systems with delays, Mathematics and Computers in Simulation, 45, 3-4, 339-348 (1998) · Zbl 1017.93506 [152] Loiseau, J. J., & Rabah, R. (1997). Analysis and control of time-delay systems. JESA. European Journal of Automatic Systems31; Loiseau, J. J., & Rabah, R. (1997). Analysis and control of time-delay systems. JESA. European Journal of Automatic Systems31 [153] Louisell, J. (1991). A stability analysis for a class of differential-delay equations having time-varying delay; Louisell, J. (1991). A stability analysis for a class of differential-delay equations having time-varying delay · Zbl 0735.34063 [154] Louisell, J., Delay differential systems with time-varying delayNew directions for stability theory, Kybernetika, 37, 3, 239-252 (2001) · Zbl 1265.93221 [155] Luck, R.; Ray, A., An observer-based compensator for distributed delays, Automatica, 26, 5, 903-908 (1990) · Zbl 0701.93055 [156] Luo, N., & De la Sen, M. (1992). State feedback sliding mode controls of a class of time-delay systems. In ACC92American control conference; Luo, N., & De la Sen, M. (1992). State feedback sliding mode controls of a class of time-delay systems. In ACC92American control conference [157] Luo, N.; De la Sen, M., State feedback sliding mode control of a class of uncertain time-delay systems, IEE Proceedings-D, 140, 4, 261-274 (1993) · Zbl 0786.93081 [158] MacDonald, N., Biological delay systems: Linear stability theory, Cambridge Studies in Mathematics Biology, Vol. 8 (1989), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0669.92001 [159] Mahmoud, M. S. (2000). Robust control and filtering for time-delay systems; Mahmoud, M. S. (2000). Robust control and filtering for time-delay systems · Zbl 0969.93002 [160] Majhi, S., & Atherton, D. (1998). A new Smith predictor and controller for unstable and integrating processes with time delay. In 37th IEEE CDC98Conference on decision and control; Majhi, S., & Atherton, D. (1998). A new Smith predictor and controller for unstable and integrating processes with time delay. In 37th IEEE CDC98Conference on decision and control [161] Majhi, S., & Atherton, D. P. (1999). A novel identifcation method for time delay processes. In ECC99Fifth European control conference; Majhi, S., & Atherton, D. P. (1999). A novel identifcation method for time delay processes. In ECC99Fifth European control conference [162] Mäkilä, P. M.; Partington, J. R., Laguerre and Kautz shift approximations of delay systems, International Journal of Control, 72, 932-946 (1999) · Zbl 0963.93042 [163] Mäkilä, P. M.; Partington, J. R., Shift operator induced approximations of delay systems, SIAM Journal of Control and Optimization, 37, 6, 1897-1912 (1999) · Zbl 0935.93047 [164] Manitius, A.; Olbrot, A. W., Finite spectrum assignment problem for systems with delays, IEEE Transactions on Automatic Control, 24, 4, 541-553 (1979) · Zbl 0425.93029 [165] Mascolo, S., Congestion control in high speed communication networks using the Smith principle, Automatica, 35, 1921-1935 (1999) · Zbl 0951.90015 [166] Mazenc, F., Mondié, S., & Niculescu, S. I. (2001). Global asymptotic stabilization for chains of integrators with a delay in the input. In 40th IEEE CDC01Conference on decision and control; Mazenc, F., Mondié, S., & Niculescu, S. I. (2001). Global asymptotic stabilization for chains of integrators with a delay in the input. In 40th IEEE CDC01Conference on decision and control [167] Megretski, A.; Rantzer, A., System analysis via integral quadratic constraints, IEEE Transactions on Automatic Control, 42, 6, 819-830 (1997) · Zbl 0881.93062 [168] Meinsma, G.; Zwart, H., On \(H_∞\) control for dead-time systems, IEEE Transactions on Automatic Control, 45, 2, 272-285 (2000) · Zbl 0978.93025 [169] Mérigot, A., & Mounier, H. (2000). Quality of service and MPEG4 video transmission. In MTNS0014th symposium on mathematical theory of networks and systems; Mérigot, A., & Mounier, H. (2000). Quality of service and MPEG4 video transmission. In MTNS0014th symposium on mathematical theory of networks and systems [170] Mirkin, L. (2000). On the extraction of dead-time controllers from delay-free parametrizations. In Second IFAC workshop on linear time delay systems; Mirkin, L. (2000). On the extraction of dead-time controllers from delay-free parametrizations. In Second IFAC workshop on linear time delay systems [171] Mirkin, L.; Tadmor, G., \(H_∞\) control of systems with I/O delayA review of some problem-oriented methods, IMA Journal of Mathematical Control and Information, 19, 1-2, 185-200 (2002) · Zbl 1015.93014 [172] Mondié, S., Niculescu, S. I., & Loiseau, J. J. (2001). Delay robustness of closed loop finite assignment for input delay systems. In Third IFAC workshop on time delay systems; Mondié, S., Niculescu, S. I., & Loiseau, J. J. (2001). Delay robustness of closed loop finite assignment for input delay systems. In Third IFAC workshop on time delay systems [173] Mondié, S., & Santos, O. (2000). Une condition nécessaire pour l’implantation de lois de commandes à retards distribuées. \(In CIFA2000^e \)IEEE conf. internat. francophone dAutomatique; Mondié, S., & Santos, O. (2000). Une condition nécessaire pour l’implantation de lois de commandes à retards distribuées. \(In CIFA2000^e \)IEEE conf. internat. francophone dAutomatique [174] Moog, C. H.; Castro-Linares, R.; Velasco-Villa, M.; Marquez-Martinez, L. A., The disturbance decoupling problem for time-delay nonlinear systems, IEEE Transactions on Automatic Control, 45, 2, 305-309 (2000) · Zbl 0972.93044 [175] Mounier, H., Mboup, M., Petit, N., Rouchon, P., & Seret, D. (1998). High speed network congestion control with a simplified time-varying delay model. In IFAC conference on systemstructurecontrol; Mounier, H., Mboup, M., Petit, N., Rouchon, P., & Seret, D. (1998). High speed network congestion control with a simplified time-varying delay model. In IFAC conference on systemstructurecontrol [176] Mounier, H.; Rouchon, P.; Rudolph, J., Some examples of linear systems with delays, JESA, European Journal of Automatic Systems, 31, 6, 911-926 (1997) [177] Mounier, H.; Rudolph, J., Flatness based control of nonlinear delay systemsA chemical reactor example, International Journal of Control, 71, 871-890 (1998) · Zbl 0938.93591 [178] Nagpal, K. M.; Ravi, R., \(H_∞\) control and estimation problems with delayed measurementsState space solutions, SIAM Journal on Control and Optimization, 35, 4, 1217-1243 (1997) · Zbl 0893.93012 [179] Nguang, S. K. (1998). Robust \(H_∞\)37th IEEE CDC98Conference on decision and control; Nguang, S. K. (1998). Robust \(H_∞\)37th IEEE CDC98Conference on decision and control [180] Nguang, S. K., Comments on “Robust stabilization of uncertain input-delay systems by SMC with delay compensation”, Automatica, 37, 1677 (2001) · Zbl 1136.93435 [181] Niculescu, S. I., \(H_∞\) memoryless control with an \(α\)-stability constraint for time delays systemsAn LMI approach, IEEE Transactions on Automatic Control, 43, 5, 739-743 (1998) · Zbl 0911.93031 [182] Niculescu, S. I., Delay effects on stability, Lecture notes in control and information sciences, Vol. 269 (2001), Springer: Springer Berlin · Zbl 0997.93001 [183] Niculescu, S. I., & Chen, J. (1999). Frequency sweeping tests for asymptotic stability: A model transformation for multiple delays. In 38th IEEE CDC99Conference on decision and control; Niculescu, S. I., & Chen, J. (1999). Frequency sweeping tests for asymptotic stability: A model transformation for multiple delays. In 38th IEEE CDC99Conference on decision and control [184] Niculescu, S. I.; De Souza, C. E.; Dugard, L.; Dion, J. M., Robust exponential stability of uncertain systems with time-varying delays, IEEE Transactions on Automatic Control, 43, 5, 743-748 (1998) · Zbl 0912.93053 [185] Niculescu, S. I.; Dion, J. M.; Dugard, L., Robust stabilization for uncertain time-delay systems containing saturating actuators, IEEE Transactions on Automatic Control, 41, 5, 742-747 (1996) · Zbl 0851.93067 [186] Niculescu, S. I.; Lozano, R., On the passivity of linear delay systems, IEEE Transactions on Automatic Control, 46, 3, 460-464 (2001) · Zbl 1056.93610 [187] Niculescu, S. I.; Richard, J. P., Analysis and design of delay and propagation systems, IMA Journal of Mathematical Control and Information, 19, 1-2, 1-227 (2002), (special issue) [188] Niculescu, S. I., Verriest, E. I., Dugard, L., & Dion, J. M. (1997). Stability and robust stability of time-delay systems: A guided tourLecture notes in control and information sciences; Niculescu, S. I., Verriest, E. I., Dugard, L., & Dion, J. M. (1997). Stability and robust stability of time-delay systems: A guided tourLecture notes in control and information sciences · Zbl 0914.93002 [189] Niemeyer, G. (1996). Using wave variables intime delayed force reflecting teleoperation; Niemeyer, G. (1996). Using wave variables intime delayed force reflecting teleoperation [190] Niemeyer, G., & Slotine, J. J. (1998). Towards force-reflecting teleoperation over the internet. In IEEE international conference on robotics and automation; Niemeyer, G., & Slotine, J. J. (1998). Towards force-reflecting teleoperation over the internet. In IEEE international conference on robotics and automation [191] Nilsson, J. (1998). Real-time control systems with delays; Nilsson, J. (1998). Real-time control systems with delays · Zbl 0908.93073 [192] Nilsson, J.; Bernhardsson, B.; Wittenmark, B., Stochastic analysis and control of real-time systems with random delays, Automatica, 34, 1, 57-64 (1998) · Zbl 0908.93073 [193] Oguchi, T., Watanabe, A., & Nakamizo, T. (1998). Input-output linearization of retarded nonlinear systems by an extended Lie derivative. In 37th IEEE CDC98Conference on decision and control; Oguchi, T., Watanabe, A., & Nakamizo, T. (1998). Input-output linearization of retarded nonlinear systems by an extended Lie derivative. In 37th IEEE CDC98Conference on decision and control · Zbl 1047.93012 [194] Ohta, Y.; Kojima, A., Formulas for Hankel singular values and vectors for a class of input delay systems, Automatica, 35, 201-215 (1999) · Zbl 0938.93027 [195] Olbrot, A. W., Algebraic criteria of controllability to zero function for linear constant time-lag systems, Control and Cybernetics, 2, 1/2, 59-77 (1973) · Zbl 0332.93011 [196] Olbrot, A. W., A sufficiently large time delay in feedback loop must destroy exponential stability of any decay rate, IEEE Transactions on Automatic Control, 29, 367-368 (1984) · Zbl 0541.93059 [197] Olbrot, A. W. (1998). Finite spectrum property and predictors. In First IFAC workshop on linear time delay systemsPlenary lecture; Olbrot, A. W. (1998). Finite spectrum property and predictors. In First IFAC workshop on linear time delay systemsPlenary lecture [198] Orlov, Y.; Belkoura, L.; Dambrine, M.; Richard, J. P., On identifiability of linear time-delay systems, IEEE Transactions on Automatic Control, 47, 8, 1319-1324 (2002) · Zbl 1364.93167 [199] Orlov, Y., Belkoura, L., Richard, J. P., & Dambrine, M. (2003). Adaptive identification of linear time-delay systems. International Journal on Robust and Nonlinear Control13; Orlov, Y., Belkoura, L., Richard, J. P., & Dambrine, M. (2003). Adaptive identification of linear time-delay systems. International Journal on Robust and Nonlinear Control13 · Zbl 1039.93013 [200] Orlov, Y. V., Optimal delay control—Part I, Automation and Remote Control, 49, 12, 1591-1596 (1988), (Transl. from Avtomatika i Telemekhnika, No. 12, 1988) · Zbl 0705.49013 [201] Orlov, Y. V., Discontinuous unit feedback control of uncertain infinite-dimensional systems, IEEE Transactions on Automatic Control, 45, 5, 834-843 (2000) · Zbl 0973.93018 [202] Orlov, Y. V.; Utkin, V. I., Sliding mode control in infinite-dimensional systems, Automatica, 6, 753-757 (1987) · Zbl 0661.93036 [203] Oucheriah, S., Robust tracking and model following of uncertain dynamic delay, IEEE Transactions on Automatic Control, 44, 7, 1473-1477 (1999) · Zbl 0955.93026 [204] Palmor, Z. J. (1996). Time-delay compensation—Smith predictor and its modifications. In W.S. Levine (Ed.), The control handbook; Palmor, Z. J. (1996). Time-delay compensation—Smith predictor and its modifications. In W.S. Levine (Ed.), The control handbook [205] Partington, J. R., Approximation of unstable infinite-dimensional systems using coprime factors, System and Control Letters, 16, 2, 89-96 (1991) · Zbl 0732.93015 [206] Pepe, P. (1996). Il controllo LQG dei sistemi con ritardo; Pepe, P. (1996). Il controllo LQG dei sistemi con ritardo [207] Perruquetti, W.; Barbot, J. P., Sliding mode control for engineers, Control Engineering Series, Vol. 11 (2002), Marcel Dekker: Marcel Dekker New York [208] Petit, N. (2000). Systèmes à Retards. Platitude en Génie des Procédés et Contrôle de Certaines Équations des Ondes; Petit, N. (2000). Systèmes à Retards. Platitude en Génie des Procédés et Contrôle de Certaines Équations des Ondes [209] Picard, P., & Lafay, J. F. (1995). Further results on controllability of linear systems with delay. In ECC95Third European control conference; Picard, P., & Lafay, J. F. (1995). Further results on controllability of linear systems with delay. In ECC95Third European control conference [210] Picard, P.; LaFay, J. F.; Kucera, V., Feedback realization of nonsingular precompensators for linear systems with delays, IEEE Transactions on Automatic Control, 42, 6, 848-852 (1997) · Zbl 0888.93029 [211] Picard, P.; Lafay, J. F.; Kucera, V., Model matching for linear systems with delays and 2-D systems, Automatica, 35, 3, 183-191 (1998) · Zbl 0937.93007 [212] Picard, P., Sename, O., & Lafay, J. F. (1996). Observers and observability indices for linear systems with delays. In CESA96IEEE-IMACS conference on computer engineering in system applications; Picard, P., Sename, O., & Lafay, J. F. (1996). Observers and observability indices for linear systems with delays. In CESA96IEEE-IMACS conference on computer engineering in system applications [213] Quet, P., Ramakrishnan, S., Ozbay, H., & Kalyanaraman, S. (2001). On the \(H_∞\)40th IEEE CDC01Conference on decision and control; Quet, P., Ramakrishnan, S., Ozbay, H., & Kalyanaraman, S. (2001). On the \(H_∞\)40th IEEE CDC01Conference on decision and control [214] Rabah, R.; Malabre, M., On the structure at infinity of linear delay systems with application to the disturbance decoupling problem, Kybernetica, 35, 668-680 (1999) · Zbl 1274.93108 [215] Ray, A., Output feedback control under randomly varying distributed delays, Journal of Guidance, Control and Dynamics, 17, 4, 701-711 (1994) · Zbl 0925.93291 [216] Razumikin, B. S., On the stability of systems with a delay, Prikladnava Matematika i Mekhanika, 20, 500-512 (1956), (in Russian) · Zbl 0075.27301 [217] Rekasius, Z. V. (1980). A stability test for systems with delays. In Proceedings on joint automatic control conference; Rekasius, Z. V. (1980). A stability test for systems with delays. In Proceedings on joint automatic control conference · Zbl 0429.93017 [218] Richard, J. P. (1998). Some trends and tools for the study of time delay systems. In Second conference IMACS-IEEE CESA98computational engineering in systems applicationsPlenary lecture; Richard, J. P. (1998). Some trends and tools for the study of time delay systems. In Second conference IMACS-IEEE CESA98computational engineering in systems applicationsPlenary lecture [219] Richard, J. P. (2000). Linear time delay systems: Some recent advances and open problems. In Second IFAC workshop on linear time delay systemsPlenary lecture; Richard, J. P. (2000). Linear time delay systems: Some recent advances and open problems. In Second IFAC workshop on linear time delay systemsPlenary lecture [220] Richard, J. P.; Gouaisbaut, F.; Perruquetti, W., Sliding mode control in the presence of delay, Kybernetica, 37, 4, 277-294 (2001) · Zbl 1265.93046 [221] Richard, J. P., Goubet, A., Tchangani, P. A., & Dambrine, M. (1997). Nonlinear delay systemsTools for a quantitative approach to stabilization. Lecture notes in control and information sciences; Richard, J. P., Goubet, A., Tchangani, P. A., & Dambrine, M. (1997). Nonlinear delay systemsTools for a quantitative approach to stabilization. Lecture notes in control and information sciences · Zbl 0918.93041 [222] Richard, J. P., & Kolmanovskii, V. (1998). Special Issue on Delay systems. Mathematics and Computers in Simulation45; Richard, J. P., & Kolmanovskii, V. (1998). Special Issue on Delay systems. Mathematics and Computers in Simulation45 [223] Roh, Y. H.; Oh, J. H., Robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation, Automatica, 35, 1681-1685 (1999) [224] Rudolph, J., & Mounier, H. (2000). Trajectory tracking for\(π\)flat nonlinear delay systems with a motor example. Lecture notes in control and information sciences; Rudolph, J., & Mounier, H. (2000). Trajectory tracking for\(π\)flat nonlinear delay systems with a motor example. Lecture notes in control and information sciences · Zbl 0971.93033 [225] Safonov, M. G., Stability and robustness of multivariable feedback systems (1980), MIT Press: MIT Press Cambridge, MA · Zbl 0552.93002 [226] Sename, O. (1994). Sur la commandabilité et le découplage des systèmes linéaires à retards; Sename, O. (1994). Sur la commandabilité et le découplage des systèmes linéaires à retards [227] Sename, O., New trends in design of observers for time-delay systems, Kybernetica, 37, 4, 427-458 (2001) · Zbl 1265.93108 [228] Shakkottai, S., Srikant, R. T., & Meyn, S. (2001). Boundedness of utility function based congestion controllers in the presence of delay. In 40th IEEE CDC01Conference on decision and control; Shakkottai, S., Srikant, R. T., & Meyn, S. (2001). Boundedness of utility function based congestion controllers in the presence of delay. In 40th IEEE CDC01Conference on decision and control [229] Shin, K. G.; Cui, X., Computing time delay and its effects on real-time control systems, IEEE Transactions on Control and System Technology, 3, 2, 218-224 (1995) [230] Shyu, K. K.; Yan, J. J., Robust stability of uncertain time-delay systems and its stabilization by variable structure control, International Journal of Control, 57, 237-246 (1993) · Zbl 0774.93066 [231] Silva, G. J., Datta, A., & Bhattacharyya, S. P. (2001). Controller design via Padé approximation can lead to instability. In 40th IEEE CDC01Conference on decision and control; Silva, G. J., Datta, A., & Bhattacharyya, S. P. (2001). Controller design via Padé approximation can lead to instability. In 40th IEEE CDC01Conference on decision and control [232] Sira-Ramirez, H., & Angulo-Nunez, M. I. (1998). On the passivity based regulation of a class of delay differential systems. In 37th IEEE CDC98Conference on decision and control; Sira-Ramirez, H., & Angulo-Nunez, M. I. (1998). On the passivity based regulation of a class of delay differential systems. In 37th IEEE CDC98Conference on decision and control [233] Slater, G. L.; Wells, W. R., On the reduction of optimal time delay systems to ordinary ones, IEEE Transactions on Automatic Control, 17, 154-155 (1972) [234] Smith, O. J.M., A controller to overcome dead time, ISA Journal of Instrument Society of America, 6, 28-33 (1959) [235] Smith, O. J. M. (1957). Posicast control of damped oscillatory systems. In Proceedings of the IRE; Smith, O. J. M. (1957). Posicast control of damped oscillatory systems. In Proceedings of the IRE [236] Sontag, E. D., The lattice of minimal realizations of response maps over rings, Mathematical Systems Theory, 11, 169-175 (1977) · Zbl 0349.93012 [237] Tadmor, G., The standard \(H_∞\) problem in systems with a single input delay, IEEE Transactions on Automatic Control, 45, 3, 382-397 (2000) · Zbl 0978.93026 [238] Tan, K. K.; Wang, Q. K.; Lee, T. H., Finite spectrum assignment control of unstable time delay processes with relay tuning, Industrial Engineering and Chemical Research, 37, 4, 1351-1357 (1998) [239] Tarbouriech, S.; Gomes Da Silva, J. M., Synthesis of controllers for continuous time delay systems with saturating controls via LMIs, IEEE Transactions on Automatic Control, 45, 1, 105-111 (2000) · Zbl 0978.93062 [240] Teel, A. R., Connection between Razumikhin-type theorems and the ISS nonlinear small gain theorem, IEEE Transactions on Automatic Control, 43, 7, 960-964 (1998) · Zbl 0952.93121 [241] Thowsen, A., An analytical stability test for a class of linear time-delay systems, IEEE Transactions on Automatic Control, 25, 735-736 (1981) · Zbl 0481.93049 [242] Tits, A. L.; Balakrishnan, V., Small-\(μ\) theorem with frequency-dependent uncertainty bounds, Mathematics of Control Signals and Systems, 11, 3, 220-243 (1998) · Zbl 0917.93016 [243] Tsoi, A. C. (1978). Recent advances in the algebraic system theory of delay differential equations; Tsoi, A. C. (1978). Recent advances in the algebraic system theory of delay differential equations · Zbl 0417.93003 [244] Tsypkin, Ya. Z., The systems with delayed feedback, Avtomatika i Telemekhnika, 7, 107-129 (1946) [245] Tuch, J.; Feuer, A.; Palmor, Z. J., Time delay estimation in continuous linear time-invariant systems, IEEE Transactions on Automatic Control, 39, 823-827 (1994) · Zbl 0807.93006 [246] Van Keulen, B., \(H_∞\) control for distributed parameter systems: A state space approach (1993), Birkhauser: Birkhauser Basel · Zbl 0788.93018 [247] VanAssche, V., Dambrine, M., Lafay, J. F., & Richard, J. P. (1999). Some problems arising in the implementation of distributed-delay control laws. In 38th IEEE CDC99Conference on decision and control; VanAssche, V., Dambrine, M., Lafay, J. F., & Richard, J. P. (1999). Some problems arising in the implementation of distributed-delay control laws. In 38th IEEE CDC99Conference on decision and control [248] Verduyn-Lunel, S. M. (1997). Identification problems in functional differential equations. In 36th IEEE CDC97Conference on decision and control; Verduyn-Lunel, S. M. (1997). Identification problems in functional differential equations. In 36th IEEE CDC97Conference on decision and control [249] Verriest, E. I. (1999). Robust stability and adaptive control of time-varying neutral systems. In 38th IEEE CDC99Conference on decision and control; Verriest, E. I. (1999). Robust stability and adaptive control of time-varying neutral systems. In 38th IEEE CDC99Conference on decision and control [250] Verriest, E. I., Stability of systems with state-dependent and random delays, IMA Journal on Mathematical Control and Information, 19, 1-2, 103-114 (2002) · Zbl 1010.34078 [251] Verriest, E. I.; Aggoune, W., Stability of nonlinear differential delay systems, Mathematics and Computers in Simulation, 45, 3-4, 257-268 (1998) · Zbl 1017.93511 [252] Walton, K.; Marshall, J. E., Direct method for TDS stability analysis, IEE Proceedings, Part D, 134, 101-107 (1987) · Zbl 0636.93066 [253] Wang, Z., Huang, B., & Unbehausen, H. (1999a). Robust \(H_∞\)IFAC 14th world congress; Wang, Z., Huang, B., & Unbehausen, H. (1999a). Robust \(H_∞\)IFAC 14th world congress [254] Wang, Z.; Huang, B.; Unbehausen, H., Robust \(H_∞\) observer design of linear state delayed systems with parametric uncertaintyThe discrete-time case, Automatica, 35, 6, 1161-1167 (1999) · Zbl 1041.93514 [255] Wang, Z. Q., & Skogestad, S. (1993). Robust controller design for uncertain time delay systems. Lecture notes in control and information sciences; Wang, Z. Q., & Skogestad, S. (1993). Robust controller design for uncertain time delay systems. Lecture notes in control and information sciences · Zbl 0793.93051 [256] Wang, Q. G.; Zhang, Y., Robust identification of continuous systems with dead-time from step responses, Automatica, 37, 377-390 (2001) · Zbl 0980.93017 [257] Watanabe, K., Nobuyama, E., & Kojima, K. (1996). Recent advances in control of time-delay systems a tutorial review. In 35th IEEE CDC96Conference on decision and control; Watanabe, K., Nobuyama, E., & Kojima, K. (1996). Recent advances in control of time-delay systems a tutorial review. In 35th IEEE CDC96Conference on decision and control [258] Weiss, L., On the controllability of delay-differential equations, SIAM Journal on Control and Optimization, 5, 4, 575-587 (1967) · Zbl 0183.16402 [259] Willems, J., The analysis of feedback systems (1971), MIT Press: MIT Press Cambridge, MA · Zbl 0244.93048 [260] Willems, J., Paradigms and puzzles in the theory of dynamical systems, IEEE Transactions on Automatic Control, 36, 259-294 (1991) · Zbl 0737.93004 [261] Wu, F.; Grigoriadis, K. M., LPV systems with parameter-varying time delaysAnalysis and control, Automatica, 37, 221-229 (2001) · Zbl 0969.93020 [262] Yamanaka, K.; Ushida, K.; Shimemura, E., Optimal control of systems with random delay, International Journal on Control, 29, 3, 489-495 (1979) · Zbl 0401.49012 [263] Yao, Y. X.; Zhang, Y. M.; Kovacevic, R., Functional observer and state feedback for input time-delay systems, International Journal on Control, 66, 4, 603-617 (1997) · Zbl 0873.93015 [264] Yoon, M. G.; Lee, B. H., A new approximation method for time-delay systems, IEEE Transactions on Automatic Control, 42, 7, 1008-1012 (1997) · Zbl 0889.93021 [265] Youcef-Toumi, K.; Ito, O., A time delay controller design for systems with unknown dynamics, ASME Journal on Dynamic Systems Measurement and Control, 112, 133-142 (1990) · Zbl 0709.93035 [266] Youcef-Toumi, K.; Reddy, S., Analysis of linear time invariant systems with time delay, ASME Journal on Dynamic Systems Measurement and Control, 114, 4, 623-633 (1992) · Zbl 0769.93051 [267] Youcef-Toumi, K.; Reddy, S., Dynamic analysis anf control of high speed and high precision active magnetic bearings, ASME Journal on Dynamic Systems Measurement and Control, 14, 4, 544-555 (1992) · Zbl 0769.93051 [268] Youcef-Toumi, K.; Wu, S. T., Input-output linearization using time delay control, ASME Journal on Dynamic Systems Measurement and Control, 114, 10-19 (1992) · Zbl 0767.93036 [269] Zhang, J., Knospe, C. R., & Tsiotras, P. (2000). Stability of linear time-delay systems: A delay-dependent criterion with a tight conservatism bound. In ACC00American control conference; Zhang, J., Knospe, C. R., & Tsiotras, P. (2000). Stability of linear time-delay systems: A delay-dependent criterion with a tight conservatism bound. In ACC00American control conference [270] Zheng, F.; Cheng, M.; Gao, W. B., Variable structure control of TDS with a simulation study on stabilizing combustion in liquid propellant rocket motors, Automatica, 31, 7, 1031-1037 (1995) · Zbl 0842.93011 [271] Zhou, K.; Khargonekar, P. P., On the weighted sensitivity minimization problem for delay systems, System and Control Letters, 8, 307-312 (1987) · Zbl 0621.93015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.