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Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays. (English) Zbl 1100.93034
Summary: We consider the problems of robust stability and stabilization via memoryless state feedback for uncertain discrete-time switched systems with mode-dependent time-varying delays. By using a descriptor system method and linear matrix inequality technique, and by introducing a switched Lyapunov functional, we establish some new delay-dependent stability and stabilization criteria for the system. Numerical examples are presented to illustrate the effectiveness of the theoretical results.

MSC:
93D09Robust stability of control systems
93C55Discrete-time control systems
93D10Popov-type stability of feedback systems
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LMI toolbox
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References:
[1] Branicky, M. S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE trans. Automat. control 43, 475-482 (1998) · Zbl 0904.93036
[2] Boyd, S.; Elghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory. (1994) · Zbl 0816.93004
[3] Dayawansa, W. P.; Martin, C. F.: A converse Lyapunov theorem for a class of dynamical systems which undergo switching. IEEE trans. Automat. control 44, 751-760 (1999) · Zbl 0960.93046
[4] Daafouz, J.; Riedinger, P.; Lung, C.: Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE trans. Automat. control 47, 1883-1887 (2002)
[5] Fridman, E.: New Lyapunov-Krasovskiń≠ functionals for stability of linear retard and neutral type systems. Syst. control lett. 43, 309-319 (2001) · Zbl 0974.93028
[6] Fridman, E.; Shaked, U.: A descriptor system approach to H$\infty $control of linear time-delay systems. IEEE trans. Automat. control 47, 253-270 (2002) · Zbl 1006.93021
[7] E. Feron, Quadratic stabilizability of switched systems via state and output feedback, Center for Intelligent Control Systems, Massachusetts Institute of Technology, Cambridge, MA, Tech. Rep. CICS P-468, Feb, 1996.
[8] Gahinet, P.; Nemirovski, V.; Laub, A. J.; Chilali, M.: LMI control toolbox for use with Matlab. (1995)
[9] Li, X.; Fridman, E.; Shaked, U.: Robust H$\infty $control of distributed delay systems with application to combustion control. IEEE trans. Automat. control 46, 1930-1935 (2001) · Zbl 1017.93038
[10] Li, Z. G.; Wen, C. Y.; Soh, Y. C.: Stabilization of a class of switched systems via designing switching laws. IEEE trans. Automat. control 46, 665-670 (2001) · Zbl 1001.93065
[11] Li, Z. G.; Wen, C. Y.; Soh, Y. C.: Observer-based stabilization of switching linear systems. Automatica 39, 517-524 (2003) · Zbl 1013.93045
[12] Liberzon, D.; Hespanha, J. P.; Morse, A. S.: Stability of switched systems: a Lie-algebraic condition. Syst. control lett. 37, 117-122 (1999) · Zbl 0948.93048
[13] Liberzon, D.; Morse, A. S.: Basic problems in stability and design of switched systems. IEEE control syst. Mag. 19, 59-70 (1999)
[14] Morse, A. S.: Control using logic-based switching. (1997) · Zbl 0864.00080
[15] Moon, Y. S.; Park, P.; Kwon, W. H.; Lee, Y. S.: Delay-dependent robust stabilization of uncertain state-delayed systems. Int. J. Control 74, 1447-1455 (2001) · Zbl 1023.93055
[16] Park, P.: A delay-dependent stability criterion for systems with uncertain time-invariant delays. IEEE trans. Automat. control 44, 876-877 (1999) · Zbl 0957.34069
[17] M.A. Wicks, P. Peleties, R.A. DeCarlo, Construction of piecewise Lyapunov functions for stabilizaing switched systems, in: Proc. IEEE Conf. on Decision and Control, Lake Buena Vista, December 1994, pp. 3492-3497.
[18] Wicks, M. A.; Peleties, P.; Decarlo, R. A.: Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems. Eur. J. Control 4, 140-147 (1998) · Zbl 0910.93062
[19] Wang, Y.; Xie, L.; De Souza, C. E.: Robust control of a class of uncertain nonlinear systems. Syst. control lett. 19, 139-149 (1972) · Zbl 0765.93015
[20] Xie, D.; Wang, L.; Hao, F.; Xie, G.: LMI approach to L2 gain analysis and control synthesis of uncertain switched systems. IEE proc. Control theory appl. 151, 21-28 (2004)
[21] G. Zhai, Quadratic stability of discrete-time switched systems via state and output feedback, in: Proc. IEEE Conf. on Decision and Control, Orlando, FL, December 2001, pp. 2165-2166.
[22] Zhai, G.; Hu, B.; Yasuda, K.; Michei, A. N.: Stability and L2 gain analysis of discrete-time switched systems. Trans. inst. Syst., control inform. Eng. 15, 117-125 (2002)