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Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay. (English) Zbl 0974.93052
Summary: This paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete-time systems with state delay. The system under consideration involves state time delay and time-varying norm-bounded parameter uncertainties appearing in all the matrices of the state-space model. Necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities, respectively. A robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities. Two examples are presented to demonstrate the effectiveness of the proposed approach.

MSC:
93D15 Stabilization of systems by feedback
93C55 Discrete-time control/observation systems
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[1] Barmish, B.R., Necessary and sufficient conditions for quadratic stabilizability of an uncertain systems, J. optim. theory appl., 46, 399-408, (1985) · Zbl 0549.93045
[2] Chou, J.H., Stability robustness of linear state space models with structured perturbations, Systems control lett., 15, 207-210, (1990) · Zbl 0724.93062
[3] Esfahani, S.H.; Moheimani, S.O.R.; Petersen, I.R., LMI approach suboptimal quadratic guaranteed cost control for uncertain time-delay systems, IEE proc. control theory appl., 145, 491-498, (1998)
[4] Garcia, G.; Bernussou, J., Pole assignment for uncertain systems in a specified disk by state feedback, IEEE trans. automat. control, 40, 184-190, (1995) · Zbl 0925.93301
[5] Garcia, G.; Bernussou, J.; Arzelier, D., Robust stabilization of discrete-time linear systems with norm-bounded time-varying uncertainty, Systems control lett., 22, 327-339, (1994) · Zbl 0820.93059
[6] Garcia, G.; Bernussou, J.; Arzelier, D., Stabilization of an uncertain linear dynamic systems by state and output feedback: a quadratic stabilizability approach, Internat. J. control, 64, 839-858, (1996) · Zbl 0857.93080
[7] Khargonekar, P.P.; Petersen, I.R.; Zhou, K., Robust stabilization of uncertain linear systems: quadratic stabilizability and H∞ control, IEEE trans. automat. control, 35, 356-361, (1990) · Zbl 0707.93060
[8] Li, X.; De Souza, C.E., Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach, IEEE trans. automat. control, 42, 1144-1148, (1997) · Zbl 0889.93050
[9] Mahmoud, M.S.; Al-Muthairi, N.F., Quadratic stabilization of continuous time systems with state-delay and norm-bounded time-varying uncertainties, IEEE trans. automat. control, 39, 2135-2139, (1994) · Zbl 0925.93585
[10] Moheimani, S.O.R.; Petersen, I.R., Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems, IEE proc. control theory appl., 144, 183-188, (1997) · Zbl 0873.49024
[11] Su, H.; Chu, J., Robust H∞ control for linear time-varying uncertain time-delay systems via dynamic output feedback, Internat. J. systems sci., 30, 1093-1107, (1999) · Zbl 1033.93507
[12] E.I. Verriest, A.F. Ivanov, Robust stability of delay-difference equations, Proceedings of the 34th IEEE Conference Decision and Control, New Orleans, LA, 1995, pp. 386-391.
[13] Wang, S.S.; Chen, B.S.; Lin, T.P., Robust stability of uncertain time-delay systems, Internat. J. control, 46, 963-976, (1987) · Zbl 0629.93051
[14] Wei, K.; Yedavalli, R.K., Robust stabilizability for linear systems with both parameter variation and unstructured uncertainty, IEEE trans. automat. control, 34, 149-156, (1989) · Zbl 0681.93054
[15] Xu, B.; Lam, J., Decentralized stabilization of large-scale interconnected time-delay systems, J. optim. theory appl., 103, 231-240, (1999) · Zbl 0945.90089
[16] Xu, S.; Yang, C., Stabilization of discrete-time singular systems: a matrix inequalities approach, Automatica, 35, 1613-1617, (1999) · Zbl 0959.93048
[17] Zeng, X.J., Robust stability for linear discrete-time systems with structured perturbations, Internat. J. control, 61, 739-748, (1995) · Zbl 0821.93061
[18] Zhou, K.; Khargonekar, K.P.P., Robust stabilization of linear systems with norm-bounded time-varying uncertainty, Systems control lett., 10, 7-20, (1998)
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