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Improved stability criterion and its applications in delayed controller design for discrete-time systems. (English) Zbl 1152.93453

Summary: This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays and the problem of stabilization for discrete-time linear systems via time-delayed controllers. The first problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality. Based on this, a sufficient condition for the solvability of the second problem is presented. The reduced conservatism of the proposed stability result is shown through a numerical example, while the applicability of the time-delayed controller design method is demonstrated by an inverted pendulum system.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C55 Discrete-time control/observation systems
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[1] Chen, B.; Lam, J.; Xu, S., Memory state feedback guaranteed cost control for neutral delay systems, International Journal of Innovative Computing, Information & Control, 2, 293-303 (2006)
[2] Chen, W. H.; Guan, Z. H.; Lu, X., Delay-dependent guaranteed cost control for uncertain discrete-time systems with delay, IEE Proceedings Part D: Control Theory and Applications, 150, 412-416 (2003)
[3] El Ghaoui, L.; Oustry, F.; Rami, A. M., A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Transactions on Automatic control, 42, 1171-1176 (1997) · Zbl 0887.93017
[4] Fridman, E.; Shaked, U., Stability and guaranteed cost control of uncertain discrete delay systems, International Journal of Control, 78, 235-246 (2005) · Zbl 1083.93045
[5] Gao, H.; Chen, T., New results on stability of discrete-time systems with time-varying state delay, IEEE Transactions on Automatic Control, 52, 328-334 (2007) · Zbl 1366.39011
[6] Gao, H.; Lam, J.; Wang, C.; Wang, Y., Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay, IEE Proceedings Part D: Control Theory and Applications, 151, 691-698 (2004)
[7] Garcia, G.; Bernussou, J.; Arzelier, D., Robust stabilization of discrete-time linear systems with norm-bounded time-varying uncertainty, Systems & Control Letters, 22, 327-339 (1994) · Zbl 0820.93059
[8] He, Y.; Wang, Q. G.; Lin, C.; Wu, M., Delay-range-dependent stability for systems with time-varying delay, Automatica, 43, 371-376 (2007) · Zbl 1111.93073
[9] Jiang, X., Han, Q. L., & Yu, X. (2005). Stability criteria for linear discrete-time systems with interval-like time-varying delay. In Proceedings of the American control conference; Jiang, X., Han, Q. L., & Yu, X. (2005). Stability criteria for linear discrete-time systems with interval-like time-varying delay. In Proceedings of the American control conference
[10] 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, 87-91 (2006) · Zbl 1366.93469
[11] Park, P., A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE Transactions on Automatic Control, 44, 876-877 (1999) · Zbl 0957.34069
[12] Peaucelle, D.; Gouaisbaut, F., Discussion on: “Parameter-dependent Lyapunov function approach to stability analysis and design for uncertain systems with time-varying delay”, European Journal of Control, 11, 69-70 (2005) · Zbl 1293.93589
[13] Xie, L.; De Souza, C. E., Robust \(H_\infty\) control for linear systems with norm-bounded time-varying uncertainty, IEEE Transactions on Automatic Control, 37, 1188-1191 (1992) · Zbl 0764.93027
[14] Xiong, J.; Lam, J., Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers, Automatica, 42, 747-753 (2006) · Zbl 1137.93421
[15] Xu, S.; Lam, J., Improved delay-dependent stability criteria for time-delay systems, IEEE Transactions on Automatic Control, 50, 384-387 (2005) · Zbl 1365.93376
[16] Zhang, B.; Zhou, S.; Xu, S., Delay-dependent \(H_\infty\) controller design for linear neutral systems with discrete and distributed delays, International Journal of Systems Sciences, 38, 611-621 (2007) · Zbl 1128.93017
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