Actas de congresos
Extended Small Gain Theorem With Application To Time-delay Switched Linear Systems
Proceedings Of The Ieee Conference On Decision And Control. , v. , n. , p. 2660 - 2665, 2012.
This paper generalizes the Small Gain Theorem - SGT to cope with time-delay switched linear systems. The main purpose is to obtain delay-dependent stability conditions that can be imposed by means of an appropriate switching strategy. Both cases of switching strategies corresponding to state and output feedback are considered. The new version of SGT is specially important in the framework of switched linear systems because it allows robustness analysis with respect to parameter or frequency domain uncertainty arising in ℍ∞ control problems and constant time-delay modeling. Since only sufficient conditions are given, the conservativeness of the final results is evaluated in terms of the gain promoted by the switching strategy, exclusively. The theory is illustrated by means of academic examples. © 2012 IEEE.26602665Elsevier,GE Global Research,MathWorks,Springer,The College of Engineering at the University of Hawaii at ManoaBliman, P.A., Stability of non-linear delay systems: Delayindependent small gain theorem and frequency domain interpretation of the Lyapunov-Krasovskii method (2002) International Journal of Control, 76, pp. 265-274Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, PhiladelphiaDeaecto, G.S., Geromel, J.C., ℋ∞ control for continuous-time switched linear systems (2010) ASME J. of Dynamic Systems, Measurement and Control, 132, pp. 041013-1/7Deaecto, G.S., Geromel, J.C., Daafouz, J., Dynamic output feedback ℋ∞ control of switched linear systems (2011) Automatica, 47, pp. 1713-1720Fridman, E., Shaked, U., Delay-dependent stability and ℋ∞ control : Constant and time-varying delays (2003) International Journal of Control, 76, pp. 48-60Fridman, E., Shaked, U., Input-output approach to stability and L2-gain analysis of systems with time-varying delays (2006) Systems & Control Letters, 55, pp. 1041-1053Geromel, J.C., Colaneri, P., Bolzern, P., Dynamic output feedback control of switched linear systems (2008) IEEE Trans. on Automat. Contr., 53, pp. 720-733He, Y., Wu, M., She, J.H., Liu, G.P., Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopictype uncertainties (2004) IEEE Trans. on Automat. Contr., 49, pp. 828-832Khalil, H.K., (1996) Nonlinear Systems, , Prentice-HallKim, S., Campbell, S., Liu, X., Stability of a class of linear switching systems with time delay (2006) IEEE Trans. on Circuits and Systems I: Regular Papers, 53, pp. 384-393Lian, J., Dimirovski, G.M., Zhao, J., Robust H∞ control of uncertain switched delay systems using multiple Lyapunov functions (2008) Proc. of 2008 American Control Conf., pp. 1582-1587. , SeattleLiberzon, D., (2003) Switching in Systems and Control, , BirkhäuserGalbusera, L., Bolzern, P., H∞-control of time-delay switched linear systems by state-dependent switching (2010) Proc. 9th IFAC Workshop on Time Delay Systems, , Prague, Czech RepublicGalbusera, L., Bolzern, P., Deaecto, G.S., Geromel, J.C., State and output feedback H∞-control of time-delay switched linear systems (2011) International Journal of Robust and Nonlinear Control, , DOI: 10.1002/rnc.1777Lin, H., Antsaklis, P.J., Stability and stabilizability of switched linear systems: A survey of recent results (2009) IEEE Trans. Automat. Contr., 54, pp. 308-322Sun, Z., Ge, S.S., (2005) Switched Linear Systems: Control and Design, , Springer, LondonSun, X.M., Wang, W., Liu, G.P., Zhao, J., Stability analysis for linear switched systems with time-varying delay (2008) IEEE Trans. on Systems, Man and Cybernetics, Part B: Cybernetics, 38, pp. 528-533Sun, X.M., Zhao, J., Hill, D., Stability and ℒ2-gain analysis for switched delay systems: A delay-dependent method (2006) Automatica, 42, pp. 1769-1774Zhang, J., Knopse, C.R., Tsiotras, P., Stability of time-delay systems: Equivalence between Lyapunov and scaled small-gain conditions (2001) IEEE Trans. Automat. Contr., 46, pp. 482-486