Abstract
In this paper, the fault-tolerant control for a class of discrete-time switched systems with time-varying delay and actuator saturation is investigated. By using a newly constructed Lyapunov functional and the average dwell time scheme, a design procedure is developed for the mode-dependent state feedback controller which ensures the exponential stability of the closed-loop systems. Moreover, an optimization problem with linear matrix inequality (LMI) constraints is formulated to estimate the domain of attraction of the origin for the underlying systems. A numerical example is finally given to illustrate the effectiveness of the proposed method.
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DeCarlo, R., Branicky, M., Pettersson, S., Lennartson, B.: Perspectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE 88, 1069–1082 (2000)
Liberzon, D.: Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. 19, 59–70 (1999)
Liberzon, D.: Switching in Systems and Control. Birkhauser, Boston (2003)
Sun, Z.D., Ge, S.S.: Switched Linear Systems: Control and Design. Springer, New York (2004)
Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control 43, 475–482 (1998)
EI-Farral, N.H., Mhaskar, P., Christofides, P.D.: Output feedback control of switched nonlinear systems using multiple Lyapunov functions. Syst. Control Lett. 54, 1163–1182 (2005)
Hespanha, J.P., Morse, A.S.: Stability of switched systems with average dwell time. In: Proceeding of the 38th IEEE Conf. Decision Contr., Phoenix, Arizona, USA, pp. 2655–2660 (1999)
Mahmoud, M.S.: Switched Time-Delay Systems. Springer, New York (2010)
Daafouz, J., Riedinger, P., Iung, C.: Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans. Autom. Control 47, 1883–1887 (2002)
Du, D., Jiang, B., Shi, P., Zhou, S.: H ∞ filtering of discrete-time switched systems with state delays via switched Lyapunov function approach. IEEE Trans. Autom. Control 52, 1520–1525 (2007)
Gao, H., Chen, T.: New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Autom. Control 52, 328–334 (2007)
Meyer, C., Schroder, S., De Doncker, R.W.: Solid-state circuit breakers and current limiters for medium-voltage systems having distributed power systems. IEEE Trans. Power Electron. 19, 1333–1340 (2004)
Wang, D., Wang, W., Shi, P., Sun, X.: Controller failure analysis for systems with interval time-varying delay: a switched method. Circuits Syst. Signal Process. 28, 389–407 (2009)
Kim, D.K., Park, P.G., Ko, J.W.: Output feedback H ∞ control of systems with communication networks using a deterministic switching system approach. Automatica 40, 1205–1212 (2004)
Zhang, W.A., Yu, L.: Modelling and control of networked control systems with both network-induced delay and packet dropout. Automatica 44, 3206–3210 (2008)
Mahmoud, M.S.: Delay-dependent H ∞ filtering of a class of switched discrete-time state delay systems. Signal Process. 88, 2709–2719 (2008)
Mahmoud, M.S., Xia, Y.: Robust stability and stabilization of a class of nonlinear switched discrete-time systems with time-varying delays. J. Optim. Theory Appl. 143, 329–355 (2009)
Phat, V.N.: Robust stability and stabilizability of uncertain linear hybrid systems with state delays. IEEE Trans. Circuits Syst. Express Briefs 52, 94–98 (2005)
Kim, S., Campbell, S.A., Liu, X.Z.: Stability of a class of switching systems with time delay. IEEE Trans. Circuits Syst. Regul. Pap. 53, 384–393 (2006)
Sun, X.M., Wang, W., Liu, G.P., Zhao, J.: Stability analysis for linear switched systems with time-varying delay. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 38, 528–533 (2008)
Sun, X.M., Zhao, J., Hill, D.J.: Stability and L 2 gain analysis for switched delay systems: a delay-dependent method. Automatica 42, 1769–1774 (2006)
Wang, D., Wang, W., Shi, P.: Exponential H ∞ filtering for switched linear systems with interval time-varying delay. Int. J. Robust Nonlinear Control 19, 532–551 (2009)
Zhang, W.A., Yu, L.: Stability analysis for discrete-time switched time-delay systems. Automatica 45, 2265–2271 (2009)
Hespanha, J.P., Naghshtabrizi, P., Xu, Y.: A survey of recent results in networked control systems. Proc. IEEE 95, 138–162 (2007)
Dai, S.L., Lin, H., Ge, S.S.: Robust stability of discrete-time switched delay systems and its application to network-based reliable control. In: Proceeding of American Control Conference. Hyatt Regency Riverfront, St. Louis, MO, USA, pp. 2367–2372 (2009)
Qiu, J., Feng, G., Yang, J.: New results on robust energy-to-peak filtering for discrete-time switched polytopic linear systems with time-varying delay. IET Control Theory Appl. 2, 795–806 (2008)
Cao, Y.Y., Lin, Z.: Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function. Automatica 39, 1235–1241 (2003)
Liu, H.P., Sun, F.C., Boukas, E.K.: Robust control of uncertain discrete-time Markovian jump systems with actuator saturation. Int. J. Control 79, 805–812 (2006)
Zhang, L.X., Boukas, E.K., Haidar, A.: Delay-range-dependent control synthesis for time-delay systems with actuator saturation. Automatica 44, 2691–2695 (2008)
Zuo, Z.Q., Ho, D.W.C., Wang, Y.J., Yang, C.L.: A new approach for estimating the domain of attraction for linear systems with time-varying delay and saturating actuators. In: Proceeding of the 7th Asian Control Conference, Hong Kong, China, pp. 274–279 (2009)
Shi, P., Boukas, E.K.: H ∞ control for Markovian jumping linear systems with parametric uncertainties. J. Optim. Theory Appl. 95, 75–99 (1997)
Shi, P., Boukas, E.K., Nguang, S.K., Guo, X.: Robust disturbance attenuation for discrete-time active fault tolerant control systems with uncertainties. Optim. Control Appl. Methods 24, 85–101 (2003)
Mahmoud, M.: Sufficient conditions for the stabilization of feedback delayed discrete time fault tolerant control systems. Int. J. Innov. Comput. Inf. Control 5, 1137–1146 (2009)
Tong, S.C., Wang, T.C., Zhang, W.: Fault tolerant control for uncertain fuzzy systems with actuator failures. Int. J. Innov. Comput. Inf. Control 4, 2461–2474 (2008)
Mahmoud, M.: Stabilizing controllers for a class of discrete time fault tolerant control systems. ICIC Express Lett. 2, 213–218 (2008)
Youssef, R., Hui, P.: Piecewise sliding mode decoupling fault tolerant control system. ICIC Express Lett. 4, 1215–1222 (2010)
Wang, Z., Wei, G., Feng, G.: Reliable H ∞ control for discrete-time piecewise linear systems with infinite distributed delays. Automatica 45, 2991–2994 (2009)
Wang, Z., Huang, L., Zuo, Y.: Reliable dissipative control for uncertain time-delayed stochastic systems with Markovian jump switching and multiplicative noise. Asian J. Control (2011). doi:10.1002/asjc.372
Lin, J., Fei, S.: Reliable control for a class of uncertain singular systems with interval time-varying delay. Asian J. Control (2010). doi:10.1002/asjc.192
Geromel, J.C., de Oliveira, M.C., Bernussou, J.: Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions. SIAM J. Control Optim. 41, 700–711 (2002)
Qiu, J., Feng, G., Yang, J.: Robust H ∞ static output feedback control of discrete-time switched polytopic linear systems with average dwell-time. Sci. China Ser. F 52, 2019–2031 (2009)
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Communicated by Po-Lung Yu.
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Zhang, D., Yu, L. Fault-Tolerant Control for Discrete-Time Switched Linear Systems with Time-Varying Delay and Actuator Saturation. J Optim Theory Appl 153, 157–176 (2012). https://doi.org/10.1007/s10957-011-9955-7
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DOI: https://doi.org/10.1007/s10957-011-9955-7