{"title":"Switching Rule for the Exponential Stability and Stabilization of Switched Linear Systems with Interval Time-varying Delays","authors":"Kreangkri Ratchagit","volume":60,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":2025,"pagesEnd":2032,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/12935","abstract":"
This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.<\/p>\r\n","references":"[1] V.N. Phat and P.T. Nam (2007), Exponential stability and stabilization\r\nof uncertain linear time-varying systems using parameter dependent\r\nLyapunov function. Int. J. of Control, 80, 1333-1341.\r\n[2] V.N. Phat and P. Niamsup, Stability analysis for a class of functional differential\r\nequations and applications. Nonlinear Analysis: Theory, Methods\r\n& Applications 71(2009), 6265-6275.\r\n[3] V.N. Phat, T. Bormat and P. Niamsup, Switching design for exponential\r\nstability of a class of nonlinear hybrid time-delay systems, Nonlinear\r\nAnalysis: Hybrid Systems, 3(2009), 1-10.\r\n[4] Y.J. Sun, Global stabilizability of uncertain systems with time-varying\r\ndelays via dynamic observer-based output feedback, Linear Algebra and\r\nits Applications, 353(2002), 91-105.\r\n[5] O.M. Kwon and J.H. Park, Delay-range-dependent stabilization of uncertain\r\ndynamic systems with interval time-varying delays, Applied Math.\r\nConputation, 208(2009), 58-68.\r\n[6] H. Shao, New delay-dependent stability criteria for systems with interval\r\ndelay, Automatica, 45(2009), 744-749.\r\n[7] J. Sun, G.P. Liu, J. Chen and D. Rees, Improved delay-range-dependent\r\nstability criteria for linear systems with time-varying delays, Automatica,\r\n46(2010), 466-470.\r\n[8] W. Zhang, X. Cai and Z. Han, Robust stability criteria for systems with\r\ninterval time-varying delay and nonlinear perturbations, J. Comput. Appl.\r\nMath., 234 (2010), 174-180.\r\n[9] V.N. Phat, Robust stability and stabilizability of uncertain linear hybrid\r\nsystems with state delays, IEEE Trans. CAS II, 52(2005), 94-98.\r\n[10] V.N. Phat and P.T. Nam (2007), Exponential stability and stabilization\r\nof uncertain linear time-varying systems using parameter dependent\r\nLyapunov function. Int. J. of Control, 80, 1333-1341.\r\n[11] V.N. Phat and P. Niamsup, Stability analysis for a class of functional differential\r\nequations and applications. Nonlinear Analysis: Theory, Methods\r\n& Applications 71(2009), 6265-6275.\r\n[12] V.N. Phat and P.T. Nam (2007), Exponential stability and stabilization\r\nof uncertain linear time-varying systems using parameter dependent\r\nLyapunov function. Int. J. of Control, 80, 1333-1341.\r\n[13] V.N. Phat and P. Niamsup, Stability analysis for a class of functional differential\r\nequations and applications. Nonlinear Analysis: Theory, Methods\r\n& Applications 71(2009), 6265-6275.\r\n[14] V.N. Phat, Y. Khongtham, and K. Ratchagit, LMI approach to exponential\r\nstability of linear systems with interval time-varying delays. Linear\r\nAlgebra and its Applications 436(2012), 243-251.\r\n[15] K. Ratchagit and V.N. Phat, Stability criterion for discrete-time systems,\r\nJ. Ineq. Appl., 2010(2010), 1-6.\r\n[16] F. Uhlig, A recurring theorem about pairs of quadratic forms and\r\nextensions, Linear Algebra Appl., 25(1979), 219-237.\r\n[17] K. Gu, An integral inequality in the stability problem of time delay\r\nsystems, in: IEEE Control Systems Society and Proceedings of IEEE\r\nConference on Decision and Control, IEEE Publisher, New York, 2000.\r\n[18] Y. Wang, L. Xie and C.E. de SOUZA, Robust control of a class of\r\nuncertain nonlinear systems. Syst. Control Lett., 1991992), 139-149.\r\n[19] S. Boyd, L.El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix\r\nInequalities in System and Control Theory, SIAM, Philadelphia, 1994.\r\n[20] J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential\r\nEquations, Springer-Verlag, New York, 1993.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 60, 2011"}