zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Time-delay systems: an overview of some recent advances and open problems. (English) Zbl 1145.93302
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.

MSC:
93-02Research monographs (systems and control)
93C23Systems governed by functional-differential equations
93B12Variable structure systems
34K20Stability theory of functional-differential equations
WorldCat.org
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, Sante Fe, NM, December 2001. · 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, Sante Fe, NM, December 2001.
[3] Abdallah, G., Dorato, P., Benitez-Read, J., & Byrne, R. (1993). Delayed positive feedback can stabilize oscillatory systems. In ACC’93 (American control conference) San Francisco, (pp. 3106-3107).
[4] Aernouts, W.; Roose, D.; Sepulchre, R.: Delayed control of a Moore-greitzer axial compressor model. International journal of bifurcation and chaos 10, No. 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. INRIA/CRAN, University of Metz, France (in French).
[6] Ailon, A.; Gil, M. I.: Stability analysis of a rigid robot with output-based controller and time-delay. Systems and control letters 40, No. 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. Research report 3422, INRIA, May 1998. · Zbl 1008.93049
[8] Al-Amer, S. H., & Al-Sunni, F. M. (2000). Approximation of time-delay systems. In ACC’00 (American control conference), Chicago, IL (pp. 2491-2495).
[9] Artstein, Z.: Linear systems with delayed controlsa reduction. IEEE transactions on automatic control 27, No. 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, No. 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, No. 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, No. 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, Longboat Key, FL, December 1998 (pp. 230-232).
[17] Belkoura, L., Richard, J. P., & Orlov, Y. (2000). Identifiability of linear time delay systems. In Second IFAC workshop on linear time delay systems, Ancona, Italy, September 2000 (pp. 173-176).
[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, Sante Fe, NM, December 2001.
[19] Bellman, R.; Cooke, K. L.: Differential difference equations. (1963) · Zbl 0105.06402
[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’01 (Conference on decision and control), Orlando, FL, December 2001 (pp. 2303-2308).
[22] Blanchini, F.; Ryan, E. P.: A razumikhin-type lemma for functional differential equations with application to adaptive control. Automatica 35, No. 5, 809-818 (1999) · Zbl 0934.93038
[23] Bonnet, C.; Partington, J. R.: Stabilization of fractional exponential systems including delays. Kybernetika 37, No. 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, No. 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 (Martynyuk ed.) (pp. 49-73). London: Taylor and Francis. · Zbl 1039.34066
[27] Boukas, E. K., & Liu, Z. K. (2002). Deterministic and stochastic time-delay systems. Control engineering. Basel: Birkhauser. · Zbl 1056.93001
[28] Brethé, D. (1997). Contribution à l’Etude de la Stabilisation des Systèmes Linéaires à Retards. IRCCyN, University of Nantes, EC Nantes, France, December 1997 (in French).
[29] Bushnell, L.: Editorial: networks and control. IEEE control system magazine 21, No. 1, 22-99 (2001)
[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$\infty $control of uncertain Markovian jump systems with time delay. IEEE transactions on automatic control 45, No. 1, 77-83 (2000) · Zbl 0983.93075
[32] Chang, P. H.; Lee, J. W.; Park, S. H.: Time delay observera robust observer for nonlinear plants. ASME journal of dynamic systems measurement and control 119, 521-527 (1997) · Zbl 0900.93047
[33] Chang, P. H., & Park, S. H. (1998). The enhanced time delay observer for nonlinear systems. In 37th IEEE CDC’98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 367-368).
[34] Chen, J.; Latchman, H. A.: Frequency sweeping tests for stability independent of delay. IEEE transactions on automatic control 40, No. 9, 1640-1645 (1995) · Zbl 0834.93044
[35] Cheres, E.; Gutman, S.; Palmor, Z. J.: Stabilization of uncertain dynamic systems including state delay. IEEE transactions on automatic control 34, No. 11, 1199-1203 (1989) · Zbl 0693.93059
[36] Choi, H. H. (1999). An LMI approach to sliding mode control design for a class of uncertain time delay systems. In ECC’99 (Fifth European control conference), Karlsruhe, Germany.
[37] Choi, H. H.; Chung, M. J.: Memoryless H$\infty $controller design for linear systems with delayed state and control. Automatica 31, No. 6, 917-919 (1995) · Zbl 0829.93021
[38] Choi, H. H.; Chung, M. J.: Observer-based H$\infty $controller design for state delayed linear systems. Automatica 32, No. 7, 1073-1075 (1996) · Zbl 0850.93215
[39] Choi, H. H.; Chung, M. J.: Robust observer-based H$\infty $controller design for linear uncertain time-delay systems. Automatica 33, No. 9, 1749-1752 (1997)
[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, No. 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, No. 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, No. 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 systems, Grenoble, France, July 1998, Plenary lecture (pp. 223-234).
[44] Dambrine, M., Gouaisbaut, F., Perruquetti, W., & Richard, J.-P. (1998). Robustness of sliding mode control under delays effects: A case study. In CESA’98 (IEEE-IMACS conference on computer engineering in system applications), Vol. 1, Tunisia, April 1998 (pp. 817-821).
[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, No. 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, No. 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, No. 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\infty filtering for uncertain linear systems with multiple time-varying state delays: An LMI approach. In 38th IEEE CDC’99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 2023-2028).
[52] Dieulot, J. Y., & Richard, J. P. (2001). Tracking control of a nonlinear system with input-dependent delay. In 40th IEEE CDC’01 (Conference on decision and control), Orlando, FL, December 2001.
[53] Dion, J. M., Dugard, L., & Niculescu, S. I. (2001). Time delay systems. Kybernetica, 37(3-4) (special issue). · 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 228 (1997)
[56] Dym, H.; Georgiou, T. T.; Smith, M. C.: Explicit formulas for optimally robust controllers for delay systems. IEEE transactions on automatic control 40, No. 4, 656-669 (1995) · Zbl 0830.93027
[57] El-Khazaly, R.: Variable structure robust control of uncertain time-delay systems. Automatica 34, No. 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 105 (1973)
[59] Engelborghs, K.; Dambrine, M.; Roose, D.: Limitations of a class of stabilization methods for delay systems. IEEE transactions on automatic control 46, No. 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, No. 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’00 (Conference on decision and control), Sydney, Australia, December 2000. · 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’01 (Sixth European control conference), Porto, Portugal, September 2001. · 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, Nantes, France (pp. 330-335).
[65] Foda, S. G.; Mahmoud, M. S.: Adaptive stabilization of delay differential systems with unknown uncertainty bounds. International journal on control 71, No. 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 209 (1996) · Zbl 0839.93003
[67] Fridman, E.: New Lyapunov-Krasovskiĭ functionals for stability of linear retarded and neutral type systems. System and control letters 43, No. 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, No. 4, 732-737 (2000)
[69] Fridman, E.; Shaked, U.: A descriptor system approach to H$\infty $control of linear time-delay systems. IEEE transactions on automatic control 47, No. 2, 253-270 (2002) · Zbl 1006.93021
[70] Fridman, E., & Shaked, U. (2003). Delay systems. International Journal of Robust and Nonlinear Control, 13(9) (special issue). · Zbl 1037.93042
[71] Fridman, L. M., Fridman, E., & Shustin, E. I. (1996). Steady modes and sliding modes in the relay control systems with time delay. In 35th IEEE CDC’96 (Conference on decision and control), Kobe, Japan (pp. 4601-4606).
[72] Fu, M., Li, H., & Niculescu, S. I. (1997). Robust stability and stabilization of time-delay systems via integral quadratic constraint approach. Lecture notes in control and information sciences, Vol. 228. London: Springer (pp. 101-116). · Zbl 0916.93068
[73] Gao, J.; Huang, B.; Wang, Z.: LMI-based robust H$\infty $control of uncertain linear jump systems with time-delays. Automatica 37, 1141-1146 (2001) · Zbl 0989.93029
[74] Ge, J. H.; Frank, P. M.; Lin, C. F.: Robust H$\infty $state feedback control for linear systems with state delay and parameter uncertainty. Automatica 32, No. 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, No. 9, 1200-1221 (1997) · Zbl 0889.93043
[77] Georgiou, T. T.; Smith, M. C.: Bezout factors and l1-optimal controllers for delay systems using a two-parameter compensator scheme. IEEE transactions on automatic control 44, No. 8, 1512-1521 (1999)
[78] Germani, A., Manes, C., & Pepe, P. (1996). Linearization of input-output mapping for nonlinear delay systems via static state feedback. In CESA’96 (IEEE-IMACS conference on computer engineering in system applications), Vol. 1, Lille, France (pp. 599-602).
[79] Germani, A., Manes, C., & Pepe, P. (1998). A state observer for nonlinear delay systems. In 37th IEEE CDC’98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 355-360).
[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, No. 2, 369-390 (1991)
[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’00 (American control conference), Chicago, IL, June 2000 (pp. 45-49).
[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 (Curtain ed.). Berlin: Springer (pp. 95-118).
[85] Glüsing-Lüerßen, H.: A behavioral approach to delay-differential systems. SIAM journal on control and optimization 35, No. 2, 480-499 (1997) · Zbl 0876.93022
[86] Glüsing-Lüerßen, H. (1997b). Realization behaviors given by delay-differential equations. In ECC’97 (Fourth European control conference), Brussels, Belgium, July 1997, pp. WE-M D6.
[87] Gorecki, H.; Fuksa, S.; Grabowski, P.; Korytowski, A.: Analysis and synthesis of time delay systems. (1989) · 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, No. 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’99 (Fifth European control conference), Karlsruhe, Germany.
[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’99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 4234-4239).
[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, Nantes, France (pp. 278-283).
[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, No. 6, 832-852 (1992)
[95] Gu, K.: Discretization schemes for Lyapunov-Krasovskiĭ functionals in time delay systems. Kybernetica 37, No. 4, 479-504 (2001) · Zbl 1265.93176
[96] Gu, K., & Niculescu, S. I. (1999). Additional dynamics in transformed time-delay systems. In 38th IEEE CDC’99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 4673-4677).
[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, No. 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, No. 1-2, 5-24 (2002) · Zbl 1005.93026
[99] Hale, J. K.; Verduyn-Lunel, S. M.: Introduction to functional differential equations. Applied mathematical sciences 99 (1993) · 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, No. 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, No. 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, No. 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, Cincinnati (pp. 2070-2075).
[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, No. 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, No. 1, 91-97 (2001) · Zbl 0965.93083
[108] Ionescu, V.; Oara, C.; Weiss, M.: Generalized Riccati theory. (1998)
[109] Ivanov, A. F., & Losson, J. (1995). Stable rapidly oscillating solutions in delay equations with negative feedback. Preprint CRM-2292, Center Research Mathematics, University of Montréal (25p). · 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 CDC’98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 4734-4739).
[112] Jankovic, M.: Control Lyapunov-razumikhin functions and robust stabilization of time delay systems. IEEE transactions on automatic control 46, No. 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, No. 3, 161-168 (1997)
[114] Jun, M., & Safonov, M. G. (2000). Stability analysis of a system with time-delayed states. In ACC’00 (American control conference), Chicago, IL (pp. 949-952).
[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, Nantes, France, March 1996 (pp. 61-78) (in French).
[116] Kato, J.: On Liapunov-razumikhin type theorems for functional differential equations. The mathematical society of Japan, Kobe, funkcialaj ekvacioj 16, No. 3, 225-239 (1973) · Zbl 0321.34056
[117] Katz, I. I. (1998). Liapunov Method in Stability of Stochastic Systems. Ural Academy of Railway, Ekaterinburg.
[118] Khan, B. Z.; Lehman, B.: Setpoint PI controllers for systems with large normalized dead time. IEEE transactions on control systems technology 4, No. 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 control, Nantes, France, 8-10 July 1998, Penary lecture (pp. 1-12).
[120] Kharitonov, V. L.; Melchior-Aguliar, D.: On delay-dependent stability conditions. System and control letters 40, No. 1, 71-76 (2000)
[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, Prague, Technical report, August 2001. · 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, No. 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, No. 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, No. 3, 795-804 (2003) · Zbl 1029.39005
[126] Kolmanovskii, V. B.; Myshkis, A.: Applied theory of functional differential equations. Mathematics and applications 85 (1992) · Zbl 0917.34001
[127] Kolmanovskii, V. B.; Myshkis, A.: Introduction to the theory and applications of functional differential equations. (1999) · Zbl 0917.34001
[128] Kolmanovskii, V. B., Niculescu, S. I., & Gu, K. (1999a). Delay effects on stability: A survey. In 38th IEEE CDC’99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 1993-1998).
[129] Kolmanovskii, V. B.; Niculescu, S. I.; Richard, J. P.: On the Liapunov-Krasovskiĭ functionals for stability analysis of linear delay systems. International journal on control 72, No. 4, 374-384 (1999) · Zbl 0952.34057
[130] Kolmanovskii, V. B.; Nosov, V. R.: Stability of functional differential equations. (1986) · Zbl 0593.34070
[131] Kolmanovskii, V. B.; Richard, J. P.: Stability of some linear systems with delay. IEEE transactions on automatic control 44, No. 5, 984-989 (1999) · Zbl 0964.34065
[132] Kolmanovskii, V. B.; Shaikhet, L. E.: Control of systems with aftereffect. Transaction of mathematical monographs 157 (1996)
[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 MTNS’98 (13th symposium on mathematical theory of networks and systems), Padova, Italy, July 1998.
[134] Krasovskii, N. N. (1963). Stability of motion. Stanford University Press, Stanford CA, USA, (translation by J. Brenner). · 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, No. 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, No. 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, Nantes, France, 1996 (pp. 19-42) (in French).
[138] Lakshmikantham, V., & Leela, S. (1969). Differential and integral inequalities, Vol. 2. New York: Academic Press. · Zbl 0177.12403
[139] Lee, J. H., Moon, Y. S., & Kwon, W. H. (1996). Robust H\infty controller for state and input delayed systems with structured uncertainties. In 35th IEEE CDC’96 (Conference on decision and control), Kobe, Japan (pp. 2092-2096).
[140] Lehman, B.: The influence of delays when averaging slow and fast oscillating systemsoverview. IMA journal of mathematical control information 19, No. 1-2, 201-216 (2002) · Zbl 1011.34001
[141] Lehman, B., & Weibel, S. P. (1998). Averaging theory for functional differential equations. In 37th IEEE CDC’98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 1352-1357).
[142] Lelevé, A., Fraisse, P., & Dauchez, P. (2001). Telerobotics over IP networks: Towards a low level real time architecture. In IROS’01 (International conference on intelligent robots and systems), Maui, Hawaii, October 2001.
[143] Lewis, R. M.: Control-delayed system properties via an ordinary model. International journal of control 30, No. 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\infty control of uncertain linear time-delay systems. In Proceedings of 13th IFAC world congress, San Francisco, CA, Vol. H (pp. 113-118).
[146] Loiseau, J. J. (1994). A 2-D transfert without minimal realization. In Sprann’94, IMACS, Lille, France (pp. 97-100).
[147] Loiseau, J. J. (1998). Algebraic tools for the control and stabilization of time-delay systems. In First IFAC workshop on linear time delay systems, Grenoble, France, July 1998, Plenary lecture (pp. 234-249).
[148] Loiseau, J. J.: Invariant factors assignment for a class of time-delay systems. Kybernetika 37, No. 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, No. 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, No. 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, No. 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 Systems, 31(6) (Special issue of JESA).
[153] Louisell, J. (1991). A stability analysis for a class of differential-delay equations having time-varying delay. Lecture Notes in Mathematics, Vol. 1475 (Busenberg and Martelli ed.), chapter Delay differential equations and dynamical systems (pp. 225-242). Berlin: Springer. · Zbl 0735.34063
[154] Louisell, J.: Delay differential systems with time-varying delaynew directions for stability theory. Kybernetika 37, No. 3, 239-252 (2001) · Zbl 1265.93221
[155] Luck, R.; Ray, A.: An observer-based compensator for distributed delays. Automatica 26, No. 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 ACC’92 (American control conference), Chicago, IL (pp. 894-895).
[157] Luo, N.; De La Sen, M.: State feedback sliding mode control of a class of uncertain time-delay systems. IEE Proceedings-D 140, No. 4, 261-274 (1993) · Zbl 0786.93081
[158] Macdonald, N.: Biological delay systems: linear stability theory. Cambridge studies in mathematics biology 8 (1989) · Zbl 0669.92001
[159] Mahmoud, M. S. (2000). Robust control and filtering for time-delay systems. Control Engineering Series. New York: Marcel Dekker. · 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 CDC’98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 1341-1345).
[161] Majhi, S., & Atherton, D. P. (1999). A novel identifcation method for time delay processes. In ECC’99 (Fifth European control conference), Karslruhe, Germany.
[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, No. 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, No. 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 CDC’01 (Conference on decision and control), Orlando, FL, December 2001.
[167] Megretski, A.; Rantzer, A.: System analysis via integral quadratic constraints. IEEE transactions on automatic control 42, No. 6, 819-830 (1997) · Zbl 0881.93062
[168] Meinsma, G.; Zwart, H.: On H$\infty $control for dead-time systems. IEEE transactions on automatic control 45, No. 2, 272-285 (2000) · Zbl 0978.93025
[169] Mérigot, A., & Mounier, H. (2000). Quality of service and MPEG4 video transmission. In MTNS’00 (14th symposium on mathematical theory of networks and systems), Perpignan, France.
[170] Mirkin, L. (2000). On the extraction of dead-time controllers from delay-free parametrizations. In Second IFAC workshop on linear time delay systems, Ancona, Italy, September 2000 (pp. 157-162).
[171] Mirkin, L.; Tadmor, G.: H$\infty $control of systems with I/O delaya review of some problem-oriented methods. IMA journal of mathematical control and information 19, No. 1-2, 185-200 (2002) · Zbl 1015.93014
[172] Mondié, S., Niculescu, S. I., & Loiseau, J. J. (2001). Delay robustness of closed loop finite assignment for input delay systems. In Third IFAC workshop on time delay systems, Sante Fe, NM, December 2001 (pp. 233-238).
[173] Mondié, S., & Santos, O. (2000). Une condition nécessaire pour l’implantation de lois de commandes à retards distribuées. In CIFA2000, 1eIEEE conf. internat. francophone d’Automatique, Lille, France, July 2000 (pp. 201-206).
[174] Moog, C. H.; Castro-Linares, R.; Velasco-Villa, M.; Marquez-Martinez, L. A.: The disturbance decoupling problem for time-delay nonlinear systems. IEEE transactions on automatic control 45, No. 2, 305-309 (2000) · Zbl 0972.93044
[175] Mounier, H., Mboup, M., Petit, N., Rouchon, P., & Seret, D. (1998). High speed network congestion control with a simplified time-varying delay model. In IFAC conference on system, structure, control, Nantes, France.
[176] Mounier, H.; Rouchon, P.; Rudolph, J.: Some examples of linear systems with delays. JESA, European journal of automatic systems 31, No. 6, 911-926 (1997)
[177] Mounier, H.; Rudolph, J.: Flatness based control of nonlinear delay systemsa chemical reactor example. International journal of control 71, 871-890 (1998) · Zbl 0938.93591
[178] Nagpal, K. M.; Ravi, R.: H$\infty $control and estimation problems with delayed measurementsstate space solutions. SIAM journal on control and optimization 35, No. 4, 1217-1243 (1997) · Zbl 0893.93012
[179] Nguang, S. K. (1998). Robust H\infty control of a class of nonlinear systems with delayed state and control: A LMI approach. In 37th IEEE CDC’98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 2384-2389).
[180] Nguang, S. K.: Comments on ”robust stabilization of uncertain input-delay systems by SMC with delay compensation”. Automatica 37, 1677 (2001) · Zbl 1136.93435
[181] Niculescu, S. I.: H$\infty $memoryless control with an ${\alpha}$-stability constraint for time delays systemsan LMI approach. IEEE transactions on automatic control 43, No. 5, 739-743 (1998) · Zbl 0911.93031
[182] Niculescu, S. I.: Delay effects on stability. Lecture notes in control and information sciences 269 (2001)
[183] Niculescu, S. I., & Chen, J. (1999). Frequency sweeping tests for asymptotic stability: A model transformation for multiple delays. In 38th IEEE CDC’99 (Conference on decision and control), Phoenix, USA, December 1999 (pp. 4678-4683).
[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, No. 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, No. 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, No. 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, No. 1-2, 1-227 (2002)
[188] Niculescu, S. I., Verriest, E. I., Dugard, L., & Dion, J. M. (1997). Stability and robust stability of time-delay systems: A guided tour. Lecture notes in control and information sciences, Vol. 228 (pp. 1-71). London: Springer. · Zbl 0914.93002
[189] Niemeyer, G. (1996). Using wave variables intime delayed force reflecting teleoperation. Ph.D. thesis, MIT, Cambridge, MA.
[190] Niemeyer, G., & Slotine, J. J. (1998). Towards force-reflecting teleoperation over the internet. In IEEE international conference on robotics and automation, Leuven, Belgium, May 1998 (pp. 1909-1915).
[191] Nilsson, J. (1998). Real-time control systems with delays. Ph.D. thesis, Department of Automatic Control, Lund Institute of Technology, Lund, Sweden. · Zbl 0908.93073
[192] Nilsson, J.; Bernhardsson, B.; Wittenmark, B.: Stochastic analysis and control of real-time systems with random delays. Automatica 34, No. 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 CDC’98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 1364-1369). · 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, No. 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 systems, Grenoble, France, July 1998, Plenary lecture (pp. 251-260).
[198] Orlov, Y.; Belkoura, L.; Dambrine, M.; Richard, J. P.: On identifiability of linear time-delay systems. IEEE transactions on automatic control 47, No. 8, 1319-1324 (2002)
[199] Orlov, Y., Belkoura, L., Richard, J. P., & Dambrine, M. (2003). Adaptive identification of linear time-delay systems. International Journal on Robust and Nonlinear Control, 13(9), 857-872 (Special issue on TDS E. Fridman and U. Shaked). · Zbl 1039.93013
[200] Orlov, Y. V.: Optimal delay control--part I. Automation and remote control 49, No. 12, 1591-1596 (1988) · Zbl 0705.49013
[201] Orlov, Y. V.: Discontinuous unit feedback control of uncertain infinite-dimensional systems. IEEE transactions on automatic control 45, No. 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, No. 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 (pp. 224-237). CRSC PressPress, Boca Raton, FL, USA.
[205] Partington, J. R.: Approximation of unstable infinite-dimensional systems using coprime factors. System and control letters 16, No. 2, 89-96 (1991) · Zbl 0732.93015
[206] Pepe, P. (1996). Il controllo LQG dei sistemi con ritardo. Department of Electrical Engineering and Univiversity l’Aquila, Italy (in Italian).
[207] Perruquetti, W.; Barbot, J. P.: Sliding mode control for engineers. Control engineering series 11 (2002)
[208] Petit, N. (2000). Systèmes à Retards. Platitude en Génie des Procédés et Contrôle de Certaines Équations des Ondes. Ecole des Mines de Paris (in French).
[209] Picard, P., & Lafay, J. F. (1995). Further results on controllability of linear systems with delay. In ECC’95 (Third European control conference, Rome) (pp. 3313-3318).
[210] Picard, P.; Lafay, J. F.; Kucera, V.: Feedback realization of nonsingular precompensators for linear systems with delays. IEEE transactions on automatic control 42, No. 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, No. 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 CESA’96 (IEEE-IMACS conference on computer engineering in system applications), Lille, France, Vol. 1, July 1996 (pp. 81-86).
[213] Quet, P., Ramakrishnan, S., Ozbay, H., & Kalyanaraman, S. (2001). On the H\infty controller design for congestion control in communication networks with a capacity predictor. In 40th IEEE CDC’01 (Conference on decision and control), Orlando, FL, December 2001 (pp. 598-603).
[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, No. 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)
[217] Rekasius, Z. V. (1980). A stability test for systems with delays. In Proceedings on joint automatic control conference. San Francisco, CA (pp. TP9-A). · Zbl 0429.93017
[218] Richard, J. P. (1998). Some trends and tools for the study of time delay systems. In Second conference IMACS-IEEE CESA’98, computational engineering in systems applications, Tunisia, April 1998, Plenary lecture (pp. 27-43).
[219] Richard, J. P. (2000). Linear time delay systems: Some recent advances and open problems. In Second IFAC workshop on linear time delay systems. Ancona, Italy, September 2000, Plenary lecture.
[220] Richard, J. P.; Gouaisbaut, F.; Perruquetti, W.: Sliding mode control in the presence of delay. Kybernetica 37, No. 4, 277-294 (2001) · Zbl 1265.93046
[221] Richard, J. P., Goubet, A., Tchangani, P. A., & Dambrine, M. (1997). Nonlinear delay systems: Tools for a quantitative approach to stabilization. Lecture notes in control and information sciences, Vol. 228 (pp. 218-240). London: Springer. · Zbl 0918.93041
[222] Richard, J. P., & Kolmanovskii, V. (1998). Special Issue on Delay systems. Mathematics and Computers in Simulation, 45 (3-4). · Zbl 1017.93507
[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) · Zbl 0931.93015
[224] Rudolph, J., & Mounier, H. (2000). Trajectory tracking for{$\pi$}-flat nonlinear delay systems with a motor example. Lecture notes in control and information sciences, Vol. 258 (Respondek ed.) (pp. 339-352). London, Isidori, Lamnabhi, Laguarrigue: Springer. · Zbl 0971.93033
[225] Safonov, M. G.: Stability and robustness of multivariable feedback systems. (1980) · Zbl 0552.93002
[226] Sename, O. (1994). Sur la commandabilité et le découplage des systèmes linéaires à retards. Laboratoire d’Automatique de Nantes, University of Nantes and EC Nantes, France (in French).
[227] Sename, O.: New trends in design of observers for time-delay systems. Kybernetica 37, No. 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 CDC’01 (Conference on decision and control), Orlando, FL, December 2001 (pp. 616-621).
[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, No. 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 CDC’01 (Conference on decision and control), Orlando, FL, December 2001 (pp. 4733-4737).
[232] Sira-Ramirez, H., & Angulo-Nunez, M. I. (1998). On the passivity based regulation of a class of delay differential systems. In 37th IEEE CDC’98 (Conference on decision and control), Tampa, FL, December 1998 (pp. 297-298).
[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, Vol. 45 (pp. 1249-1255).
[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$\infty $problem in systems with a single input delay. IEEE transactions on automatic control 45, No. 3, 382-397 (2000) · Zbl 0978.93026
[238] Tan, K. K.; Wang, Q. K.; Lee, T. H.: Finite spectrum assignment control of unstable time delay processes with relay tuning. Industrial engineering and chemical research 37, No. 4, 1351-1357 (1998)
[239] Tarbouriech, S.; Da Silva, J. M. Gomes: Synthesis of controllers for continuous time delay systems with saturating controls via lmis. IEEE transactions on automatic control 45, No. 1, 105-111 (2000) · Zbl 0978.93062
[240] Teel, A. R.: Connection between razumikhin-type theorems and the ISS nonlinear small gain theorem. IEEE transactions on automatic control 43, No. 7, 960-964 (1998) · Zbl 0952.93121
[241] Thowsen, A.: An analytical stability test for a class of linear time-delay systems. IEEE transactions on automatic control 25, 735-736 (1981) · Zbl 0481.93049
[242] Tits, A. L.; Balakrishnan, V.: Small-${\mu}$ theorem with frequency-dependent uncertainty bounds. Mathematics of control signals and systems 11, No. 3, 220-243 (1998) · Zbl 0917.93016
[243] Tsoi, A. C. (1978). Recent advances in the algebraic system theory of delay differential equations. Recent theoretical developments in control (Gregson ed.) (pp. 67-127). New York: Academic Press. · 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$\infty $control for distributed parameter systems: A state space approach. (1993) · Zbl 0788.93018
[247] VanAssche, V., Dambrine, M., Lafay, J. F., & Richard, J. P. (1999). Some problems arising in the implementation of distributed-delay control laws. In 38th IEEE CDC’99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 4668-4672).
[248] Verduyn-Lunel, S. M. (1997). Identification problems in functional differential equations. In 36th IEEE CDC’97 (Conference on decision and control), San Diego, CA, December 1997 (pp. 4409-4413).
[249] Verriest, E. I. (1999). Robust stability and adaptive control of time-varying neutral systems. In 38th IEEE CDC’99 (Conference on decision and control), Phoenix, AZ, December 1999 (pp. 4690-4695).
[250] Verriest, E. I.: Stability of systems with state-dependent and random delays. IMA journal on mathematical control and information 19, No. 1-2, 103-114 (2002) · Zbl 1010.34078
[251] Verriest, E. I.; Aggoune, W.: Stability of nonlinear differential delay systems. Mathematics and computers in simulation 45, No. 3-4, 257-268 (1998) · Zbl 1017.93511
[252] Walton, K.; Marshall, J. E.: Direct method for TDS stability analysis. IEE Proceedings, part D 134, 101-107 (1987) · Zbl 0636.93066
[253] Wang, Z., Huang, B., & Unbehausen, H. (1999a). Robust H\infty observer design for uncertain time-delay systems: (I) the continuous case. In IFAC 14th world congress, Beijing, China (pp. 231-236).
[254] Wang, Z.; Huang, B.; Unbehausen, H.: Robust H$\infty $observer design of linear state delayed systems with parametric uncertaintythe discrete-time case. Automatica 35, No. 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, Vol. 185 (Curtain, Bensoussan and Lions ed.) (pp. 610-622). Berlin: Springer. · 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 CDC’96 (Conference on decision and control), Kobe, Japan, December 1996 (pp. 2083-2089).
[258] Weiss, L.: On the controllability of delay-differential equations. SIAM journal on control and optimization 5, No. 4, 575-587 (1967) · Zbl 0183.16402
[259] Willems, J.: The analysis of feedback systems. (1971) · 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, No. 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, No. 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, No. 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, No. 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, No. 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 ACC’00 (American control conference), Chicago, IL, June 2000 (pp. 1458-1462).
[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, No. 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