Fault-tolerant control for discrete-time switched linear systems with time-varying delay and actuator saturation. (English) Zbl 1237.93050

Summary: 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.


93B35 Sensitivity (robustness)
93C55 Discrete-time control/observation systems
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C05 Linear systems in control theory
Full Text: DOI


[1] 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)
[2] Liberzon, D.: Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. 19, 59–70 (1999) · Zbl 1384.93064
[3] Liberzon, D.: Switching in Systems and Control. Birkhauser, Boston (2003) · Zbl 1036.93001
[4] Sun, Z.D., Ge, S.S.: Switched Linear Systems: Control and Design. Springer, New York (2004) · Zbl 1075.93001
[5] Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control 43, 475–482 (1998) · Zbl 0904.93036
[6] 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) · Zbl 1129.93497
[7] 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)
[8] Mahmoud, M.S.: Switched Time-Delay Systems. Springer, New York (2010) · Zbl 1229.93001
[9] 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) · Zbl 1364.93559
[10] 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) · Zbl 1366.93652
[11] 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) · Zbl 1366.39011
[12] 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)
[13] 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) · Zbl 1169.93341
[14] 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) · Zbl 1056.93527
[15] 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) · Zbl 1153.93321
[16] Mahmoud, M.S.: Delay-dependent H filtering of a class of switched discrete-time state delay systems. Signal Process. 88, 2709–2719 (2008) · Zbl 1151.93338
[17] 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) · Zbl 1176.93058
[18] 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)
[19] 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) · Zbl 1374.94950
[20] 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)
[21] 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) · Zbl 1114.93086
[22] 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) · Zbl 1160.93328
[23] Zhang, W.A., Yu, L.: Stability analysis for discrete-time switched time-delay systems. Automatica 45, 2265–2271 (2009) · Zbl 1179.93145
[24] Hespanha, J.P., Naghshtabrizi, P., Xu, Y.: A survey of recent results in networked control systems. Proc. IEEE 95, 138–162 (2007)
[25] 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)
[26] 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)
[27] 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) · Zbl 1139.93342
[28] 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) · Zbl 1330.93238
[29] 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) · Zbl 1155.93350
[30] 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)
[31] Shi, P., Boukas, E.K.: H control for Markovian jumping linear systems with parametric uncertainties. J. Optim. Theory Appl. 95, 75–99 (1997) · Zbl 1026.93504
[32] 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) · Zbl 1073.93568
[33] 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)
[34] 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)
[35] Mahmoud, M.: Stabilizing controllers for a class of discrete time fault tolerant control systems. ICIC Express Lett. 2, 213–218 (2008)
[36] Youssef, R., Hui, P.: Piecewise sliding mode decoupling fault tolerant control system. ICIC Express Lett. 4, 1215–1222 (2010)
[37] Wang, Z., Wei, G., Feng, G.: Reliable H control for discrete-time piecewise linear systems with infinite distributed delays. Automatica 45, 2991–2994 (2009) · Zbl 1192.93030
[38] 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 · Zbl 1219.93144
[39] 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 · Zbl 1219.93105
[40] 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) · Zbl 1022.93048
[41] 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) · Zbl 1182.93057
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.