×
Gao, Huijun; Chen, Tongwen; Lam, James

A new delay system approach to network-based control. (English) Zbl 1138.93375

Automatica 44, No. 1, 39-52 (2008).
Summary: This paper presents a new delay system approach to network-based control. This approach is based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. Firstly, new results on stability and \(\mathcal H _{\infty}\) performance are proposed for systems with two successive delay components, by exploiting a new Lyapunov-Krasovskii functional and by making use of novel techniques for time-delay systems. An illustrative example is provided to show the advantage of these results. The second part of this paper utilizes the new model to investigate the problem of network-based control, which has emerged as a topic of significant interest in the control community. A sampled-data networked control system with simultaneous consideration of network induced delays, data packet dropouts and measurement quantization is modeled as a nonlinear time-delay system with two successive delay components in the state and, the problem of network-based \(\mathcal H _{\infty}\) control is solved accordingly. Illustrative examples are provided to show the advantage and applicability of the developed results for network-based controller design.

Cited in 309 Documents

MSC:

93C57 Sampled-data control/observation systems
93B35 Sensitivity (robustness)
93D20 Asymptotic stability in control theory
93C05 Linear systems in control theory

Keywords:

linear matrix inequality (LMI); networked control systems (NCSs); sampled-data systems; stability; time-delay systems
PDF BibTeX XML Cite
\textit{H. Gao} et al., Automatica 44, No. 1, 39--52 (2008; Zbl 1138.93375)
Full Text: DOI

References:

[1] Antsaklis, P.; Baillieul, J., Guest editorial Special issue on networked control systems, IEEE Transactions on Automatic Control, 31, 9, 1421-1423 (2004) · Zbl 1365.93005
[2] Biernacki, R. M.; Hwang, H.; Battacharyya, S. P., Robust stability with structured real parameter perturbations, IEEE Transactions on Automatic Control, 32, 495-506 (1987)
[3] El Ghaoui, L.; Oustry, F.; Rami, M. A., A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Transactions on Automatic Control, 42, 8, 1171-1176 (1997) · Zbl 0887.93017
[4] Elia, N.; Mitter, S. K., Stabilization of linear systems with limited information, IEEE Transactions on Automatic Control, 46, 9, 1384-1400 (2001) · Zbl 1059.93521
[5] Fridman, E.; Shaked, U., Delay-dependent stability and \(H_\infty\) control: constant and time-varying delays, International Journal of Control, 76, 1, 48-60 (2003) · Zbl 1023.93032
[6] Fu, M.; Xie, L., The sector bound approach to quantized feedback control, IEEE Transactions on Automatic Control, 50, 11, 1698-1711 (2005) · Zbl 1365.81064
[7] Gao, H.; Lam, J.; Wang, C.; Xu, S., \(H_\infty\) model reduction for discrete time-delay systems: Delay independent and dependent approaches, International Journal of Control, 77, 321-335 (2004) · Zbl 1066.93009
[8] Gao, H.; Wang, C., Comments and further results on A descriptor system approach to \(H_\infty\) control of linear time-delay systems, IEEE Transactions on Automatic Control, 48, 3, 520-525 (2003) · Zbl 1364.93211
[9] Gao, H.; Wang, C., A delay-dependent approach to robust \(H_\infty\) filtering for uncertain discrete-time state-delayed systems, IEEE Transactions of Signal Processing, 52, 6, 1631-1640 (2004) · Zbl 1369.93175
[10] Goodwin, G. C.; Haimovich, H.; Quevedo, D. E.; Welsh, J. S., A moving horizon approach to networked control system design, IEEE Transactions on Automatic Control, 49, 9, 1427-1445 (2004) · Zbl 1365.93172
[11] Gu, K.; Kharitonov, V. L.; Chen, J., Stability of time-delay systems (2003), Springer: Springer Berlin · Zbl 1039.34067
[12] Hale, J.; Lunel, S. M.V., Introduction to functional differential equations (1993), Springer: Springer Berlin · Zbl 0787.34002
[13] He, Y.; Wang, Q.-G.; Lin, C.; Wu, M., Delay-range-dependent stability for systems with time-varying delay, Automatica, 43, 2, 371-376 (2007) · Zbl 1111.93073
[14] He, Y.; Wang, Q. G.; Xie, L. H.; Lin, C., Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE Transactions on Automatic Control, 52, 2, 293-299 (2007) · Zbl 1366.34097
[15] He, Y.; Wu, M.; She, J. H.; Liu, G. P., Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties, IEEE Transactions on Automatic Control, 49, 5, 828-832 (2004) · Zbl 1365.93368
[16] Hua, C.; Guan, X.; Shi, P., Robust backstepping control for a class of time delayed systems, IEEE Transactions on Automatic Control, 50, 6, 894-899 (2005) · Zbl 1365.93054
[18] Jing, X. J.; Tan, D. L.; Wang, Y. C., An LMI approach to stability of systems with severe time-delay, IEEE Transactions on Automatic Control, 49, 7, 1192-1195 (2004) · Zbl 1365.93226
[19] Kim, J.-H., Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty, IEEE Transactions on Automatic Control, 46, 5, 789-792 (2001) · Zbl 1008.93056
[20] Lam, J.; Gao, H.; Wang, C., Stability analysis for continuous systems with two additive time-varying delay components, Systems Control Letters, 56, 1, 16-24 (2007) · Zbl 1120.93362
[22] Lian, F.-L.; Moyne, J.; Tilbury, D., Modelling and optimal controller design of networked control systems with multiple delays, International Journal of Control, 76, 6, 591-606 (2003) · Zbl 1050.93038
[23] Lin, C.; Wang, Q.-G.; Lee, T. H., A less conservative robust stability test for linear uncertain time-delay systems, IEEE Transactions on Automatic Control, 51, 1, 87-91 (2006) · Zbl 1366.93469
[24] Liu, H.; Sun, F.; He, K.; Sun, Z., Design of reduced-order \(H_\infty\) filter for Markovian jumping systems with time delay, IEEE Transactions on Circuits and Systems (II), 51, 607-612 (2004)
[25] Montestruque, L. A.; Antsaklis, P., Stability of model-based networked control systems with time-varying transmission times, IEEE Transaction on Automatic Control, 49, 9, 1562-1572 (2004) · Zbl 1365.90039
[26] Niculescu, S. I., Delay effects on stability: a robust control approach (2001), Springer: Springer Germany, Heidelberg
[27] Richard, J. P., Time-delay systems: An overview of some recent advances and open problems, Automatica, 39, 10, 1667-1694 (2003) · Zbl 1145.93302
[28] Seiler, P.; Sengupta, R., An \(H_\infty\) approach to networked control, IEEE Transactions on Automatic Control, 50, 3, 356-364 (2005) · Zbl 1365.93147
[29] Walsh, G. C.; Ye, H.; Bushnell, L., Stability analysis of networked control systems, IEEE Transactions on Control Systems Technology, 10, 3, 438-446 (2002)
[30] Wang, Z.; Burnham, K. J., Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation, IEEE Transactions on Signal Processing, 49, 4, 794-804 (2001)
[31] Wang, Z.; Huang, B.; Unbehauen, H., Robust \(H_\infty\) observer design of linear state delayed systems with parametric uncertainty: the discrete-time case, Automatica, 35, 1161-1167 (1999) · Zbl 1041.93514
[32] Wu, M.; He, Y.; She, J. H.; Liu, G. P., Delay-dependent criteria for robust stability of time-varying delay systems, Automatica, 40, 1435-1439 (2004) · Zbl 1059.93108
[33] Xia, Y.; Jia, Y., Robust stability functionals of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functions, International Journal of Control, 75, 1427-1434 (2002) · Zbl 1078.93054
[34] Xu, S.; Lam, J.; Huang, S.; Yang, C., \(H_\infty\) model reduction for linear time-delay systems: Continuous-time case, International Journal of Control, 74, 11, 1062-1074 (2001) · Zbl 1022.93008
[35] Yang, F. W.; Wang, Z. D.; Hung, Y. S.; Gani, M., \(H_\infty\) control for networked systems with random communication delays, IEEE Transactions on Automatic Control, 51, 3, 511-518 (2006) · Zbl 1366.93167
[36] Yu, M.; Wang, L.; Chu, T., Sampled-data stabilization of networked control systems with nonlinearity, IEE Proceedings Part D: Control Theory and Applications, 152, 6, 609-614 (2005)
[37] Yu, M.; Wang, L.; Chu, T.; Hao, F., Stabilization of networked control systems with data packet dropout and transmission delays: Continuous-time case, European Journal of Control, 11, 1, 40-55 (2005) · Zbl 1293.93622
[38] Yue, D.; Han, Q.-L.; Lam, J., Network-based robust \(H_\infty\) control of systems with uncertainty, Automatica, 41, 6, 999-1007 (2005) · Zbl 1091.93007
[39] Yue, D.; Han, Q.-L.; Peng, C., State feedback controller design of networked control systems, IEEE Transactions on Circuits and Systems (II), 51, 11, 640-644 (2004)
[40] Zhang, L.; Shi, Y.; Chen, T.; Huang, B., A new method for stabilization of networked control systems with random delays, IEEE Transactions on Automatic Control, 50, 8, 1177-1181 (2005) · Zbl 1365.93421
[41] Zhang, W.; Branicky, M.; Phillips, S., Stability of networked control systems, IEEE Control Systems Magazine, 21, 84-99 (2001)
[42] Zhang, X.-M.; Wu, M.; She, J.-H.; He, Y., Delay-dependent stabilization of linear systems with time-varying state and input delays, Automatica, 41, 8, 1405-1412 (2005) · Zbl 1093.93024
[43] Zhivoglyadov, P. V.; Middleton, R. H., Networked control design for linear systems, Automatica, 39, 4, 743-750 (2003) · Zbl 1022.93018
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.