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Robust passive control for uncertain discrete-time systems with time-varying delays. (English) Zbl 1147.93034
Summary: The problem of robust passive control for uncertain discrete systems with time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and measured output matrices. Attention is focused on the design of a state feedback controller and a dynamic output feedback controller which guarantees the passivity of the closed-loop system for all admissible uncertainties. In terms of a linear matrix inequality, a sufficient condition for the solvability of this problem is presented, which is dependent on the size of the delay. When the linear matrix inequality is feasible, the explicit expression of the desired state feedback controller and output feedback controller are given. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

93D09 Robust stability
93C55 Discrete-time control/observation systems
Full Text: DOI
[1] Xu, S.; Van Dooren, P.; Stefan, R.; Lam, J., Robust stability and stabilization for singular systems with state delay and parameter uncertainty, IEEE trans automat control, 47, 7, 1122-1128, (2002) · Zbl 1364.93723
[2] Li, X.; de Souza, C.E., Criteria for robust stability and stabilization of uncertain linear systems with state-delay, Automatica, 33, 9, 1657-1662, (1997)
[3] Sun, Jitao, Delay-dependent stability criteria for time-delay chaotic systems via time-delay feedback control, Chaos, solitons & fractals, 21, 1, 143-150, (2004) · Zbl 1048.37509
[4] Choi, H.H.; Chung, M.J., An LMI approach to H∞ controller design for linear time-delay systems, Automatica, 33, 4, 737-739, (1997) · Zbl 0875.93104
[5] Chen JL, Lee L. Passivity approach to feedback connection stability for discrete-time descriptor systems. In: Proceedings of the IEEE conference on decision and control, vol. 3. 2001. p. 2865-6.
[6] Mahmoud, M.S.; Ismail, A., Passivity analysis and synthesis of discrete-time delay systems, Dynam contin discrete impuls syst ser A: math anal, 11, 4, 525-544, (2004) · Zbl 1175.93141
[7] Boyd, S.; Ghaoui, L.El.; Feron, E.; Balakrishnan, V., ()
[8] Zhang, Qiang; Wei, Xiaopeng; Xu, Jin, Delay-dependent exponential stability of cellular neural networks with time-varying delays, Chaos, solitons & fractals February, 23, 4, 1363-1369, (2005) · Zbl 1094.34055
[9] Mahmoud, M.S.; Xie, L., Passivity analysis and synthesis for uncertain time-delay systems, Math problems eng, 7, 5, 455-484, (2001) · Zbl 1014.93038
[10] Sun, W.; Khargonekar, P.P.; Shim, D., Solution to the positive real control problem for linear time-invariant systems, IEEE trans automat control, 39, 10, 2034-2046, (1994) · Zbl 0815.93032
[11] Esfahani, S.H.; Petersen, I.R., An LMI approach to output-feedback-guaranteed cost control for uncertain time-delay systems, Int J robust nonlinear control, 10, 3, 157-174, (2000) · Zbl 0951.93032
[12] Byrnes, C.I.; Isidori, A.; Willems, J.C., Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems, IEEE trans automat control, 36, 11, 1228-1240, (1991) · Zbl 0758.93007
[13] Jeung, E.T.; Kim, J.H.; Park, H.B., H∞ output feedback controller design for linear systems with time-varying delayed state, IEEE trans automat control, 43, 7, 971-974, (1998) · Zbl 0952.93032
[14] Xie, L., Output feedback H∞ control of systems with parameter uncertainty, Int J control, 63, 741-750, (1996) · Zbl 0841.93014
[15] Kolmanovskii, V.B.; Myshkis, A.D., Applied theory of functional differential equations, (1992), Kluwer Academic Publishers Dordrecht · Zbl 0907.39012
[16] Mahmoud, M.S.; Zribi, M., Passive control synthesis for uncertain systems with multiple-state delays, Comput electrical eng, 28, 3, 195-216, (2002) · Zbl 1047.93020
[17] Mahmoud MS. Passive control synthesis for uncertain time-delay systems. In: Proceedings of the 37th IEEE conference on decision and control, Tampa, USA, 1998. p. 4139-43.
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