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Stability and \(L_{2}\)-gain analysis for switched delay systems: a delay-dependent method. (English) Zbl 1114.93086
Summary: In this paper, we study stability and \(L_{2}\)-gain for a class of switched systems with time-varying delays. Sufficient conditions for exponential stability and weighted \(L_{2}\)-gain are developed for a class of switching signals with average dwell time. These conditions are delay-dependent and are given in the form of linear matrix inequalities (LMIs). As a special case of such switching signals, we can obtain exponential stability and normal \(L_{2}\)-gain under arbitrary switching signals. The state decay estimate is explicitly given. Two examples illustrate the effectiveness and applicability of the proposed method.

MSC:
93D20 Asymptotic stability in control theory
93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
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[1] Fridman, E.; Shaked, U., An improved stabilization method for linear time-delay systems, IEEE transactions on automatic control, 47, 1931-1937, (2002) · Zbl 1364.93564
[2] Gao, H.J.; Wang, C.H., Delay-dependent robust and filtering for a class of uncertain nonlinear time-delay systems, IEEE transactions on automatic control, 48, 1661-1665, (2003) · Zbl 1364.93210
[3] Hale, J.K.; Lunel, S.M.V., Introduction to functional differential equations, (1993), Springer New York
[4] Han, Q.L.; Gu, K.Q., On robust stability of time-delay systems with norm-bounded uncertainty, IEEE transactions on automatic control, 46, 1426-1431, (2001) · Zbl 1006.93054
[5] He, Y.; Wu, M.; She, J.H.; Liu, G.P., Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Systems and control letters, 51, 57-65, (2004) · Zbl 1157.93467
[6] 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, 828-832, (2004) · Zbl 1365.93368
[7] Hespanha, J. P., & Morse, A. S. (1999). Stability of switched systems with average dwell-time. 38th IEEE conference on decision and control (pp. 2655-2660), Phoenix, AZ, USA.
[8] Johansson, M.; Rantzer, A., Computation of piecewise quadratic Lyapunov functions for hybrid systems, Automatica, 43, 555-559, (1998) · Zbl 0905.93039
[9] Kim, D.K.; Park, P.G.; Ko, J.W., Output-feedback \(H_\infty\) control of systems over communication networks using a deterministic switching system approach, Automatica, 40, 1205-1212, (2004) · Zbl 1056.93527
[10] Liberzon, D., Switching in systems and control, (2003), Birkhauser Boston · Zbl 1036.93001
[11] Meyer, C.; Schroder, S.; De Doncker, R.W., Solid-state circuit breakers and current limiters for medium-voltage systems having distributed power systems, IEEE transactions on power electronics, 19, 1333-1340, (2004)
[12] Michiels, W.; Assche, V.V.; Niculescu, S.I., Stabilization of time-delay systems with a controlled time-varying delay and applications, IEEE transactions on automatic control, 50, 493-504, (2005) · Zbl 1365.93411
[13] Sun, Z.D.; Ge, S.S., Switched linear systems—control and design, (2004), Springer New York
[14] Wang, Z.D.; Huang, B.; Unbehauen, H., Robust reliable control for a class of uncertain nonlinear state-delayed systems, Automatica, 35, 955-963, (1999) · Zbl 0945.93605
[15] Xie, G. M., & Wang, L. (2004). Stability and stabilization of switched linear systems with state delay: Continuous-time case. The 16th mathematical theory of networks and systems conference, Catholic University of Leuven.
[16] Zhai, G.S.; Hu, B.; Yasuda, K.; Michel, A., Disturbance attenuation properties of time-controlled switched systems, Journal of the franklin institute, 338, 765-779, (2001) · Zbl 1022.93017
[17] Zhai, G. S., Sun, Y., Chen, X. K., & Anthony, N. M. (2003). Stability and \(L_2\) gain analysis for switched symmetric systems with time delay. American control conference (pp. 2682-2687), Denver, CO, USA.
[18] Zhao, J., & Hill David, J. (2005). On stability and \(L_2\) gain for switched systems. 44th IEEE conference on decision and control (pp. 3279-3284), Seville, Spain.
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