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Finite-time boundedness analysis for a class of switched linear systems with time-varying delay. (English) Zbl 1406.93151
Summary: The problem of finite-time boundedness for a class of switched linear systems with time-varying delay and external disturbance is investigated. First of all, the multiply Lyapunov function of the system is constructed. Then, based on the Jensen inequality approach and the average dwell time method, the sufficient conditions which guarantee the system is finite-time bounded are given. Finally, an example is employed to verify the validity of the proposed method.
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] Sun, Y., Delay-independent stability of switched linear systems with unbounded time-varying delays, Abstract and Applied Analysis, 2012, (2012) · Zbl 1242.93106
[2] Liberzon, D., Switching in Systems and Control, (2003), Boston, Mass, USA: Birkhäuser, Boston, Mass, USA · Zbl 1036.93001
[3] Sun, H. F.; Zhao, J.; Gao, X. D., Stability of switched linear systems with delayed perturbation, Control and Decision, 17, 4, 431-434, (2002)
[4] Li, Z.; Soh, Y.; Wen, C., Switched and Impulsive Systems: Analysis, Design, and Applications, 313, (2005), Berlin, Germany: Springer, Berlin, Germany
[5] Goebel, R.; Sanfelice, R. G.; Teel, A. R., Hybrid dynamical systems: robust stability and control for systems that combine continuous-time and discrete-time dynamics, IEEE Control Systems Magazine, 29, 2, 28-93, (2009) · Zbl 1395.93001
[6] Margaliot, M.; Hespanha, J. P., Root-mean-square gains of switched linear systems: a variational approach, Automatica, 44, 9, 2398-2402, (2008) · Zbl 1153.93339
[7] Shorten, R.; Wirth, F.; Mason, O.; Wulff, K.; King, C., Stability criteria for switched and hybrid systems, SIAM Review, 49, 4, 545-592, (2007) · Zbl 1127.93005
[8] Lee, J.-W.; Khargonekar, P. P., Optimal output regulation for discrete-time switched and Markovian jump linear systems, SIAM Journal on Control and Optimization, 47, 1, 40-72, (2008) · Zbl 1158.49036
[9] Branicky, M. S.; Borkar, V. S.; Mitter, S. K., A unified framework for hybrid control: model and optimal control theory, IEEE Transactions on Automatic Control, 43, 1, 31-45, (1998) · Zbl 0951.93002
[10] Lu, J. N.; Zhao, G. Y., Stability analysis based on LMI for switched systems with time delay, Journal of Southern Yangtze University, 5, 2, 171-173, (2006)
[11] Zhao, L. Y.; Zhang, Z. Q., Stability analysis of a class of switched systems with time delay, Control and Decision, 26, 7, 1113-1116, (2011)
[12] Lian, J.; Mu, C.; Shi, P., Asynchronous H-infinity Filtering for switched stochastic systems with time-varying delay, Information Sciences, 200-212, (2013) · Zbl 1293.93268
[13] Sun, Y., Stabilization of switched systems with nonlinear impulse effects and disturbances, IEEE Transactions on Automatic Control, 56, 11, 2739-2743, (2011) · Zbl 1368.93566
[14] Lin, X.; Du, H.; Li, S., Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance, Applied Mathematics and Computation, 5982-5993, (2011) · Zbl 1218.34082
[15] Hespanha, J. P.; Morse, A. S., Stability of switched systems with average dwell-time, Proceedings of the IEEE Conference on Decision and Control
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