Robust exponential stability and stabilization of linear uncertain polytopic time-delay systems
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This paper proposes new sufficient conditions for the exponential stability and stabilization of linear uncertain polytopic time-delay systems. The conditions for exponential stability are expressed in terms of Kharitonov-type linear matrix inequalities (LMIs) and we develop control design methods based on LMIs for solving stabilization problem. Our method consists of a combination of the LMI approach and the use of parameter-dependent Lyapunov functionals, which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. Numerical examples illustrating the conditions are given.
KeywordsPolytopic time-delay system Exponential stability Stabilization Parameter-dependent Lyapunov function Linear matrix inequalities
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- E. N. Chukwu. Stability and Time-Optimal Control of Hereditary Systems[M]. Boston, San Diego, New York: Academic Press, Inc., 1992.Google Scholar
- V. N. Phat, P. T. Nam. Exponential stability criteria of linear non-autonomous systems with multiple delays[J]. Electronic Journal of Differencial Equations, 2005, 2005(58): 1–9.Google Scholar
- T. Yoshizawa. Stability Theory by Lyapunov’s Second Method[M]. Tokyo: Publication of the Mathematic Society, 1966.Google Scholar
- S. Boyd, L. El Ghaou, E. Feron, et al. Linear matrix inequalities in system and control theory[M]//Studies in Applied Mathematics, Philadenphia: SIAM, 1994.Google Scholar
- A. G. Spark. Analysis of affinely parameter-varying systems using parameter dependent Lyapunov functions[C]//Proceedings Conference on Decision and Control. California, USA: IEEE, 997: 990–991.Google Scholar
- Y. Jia. Alternative proofs for inproved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty: a predective approach[J]. IEEE Transactions on Automatic Control, 2003, 48(10): 1413–1416.Google Scholar
- K. Tanaka, T. Hori, H. O. Wang. A multiple Lyapunov function approach to stabilization of fuzzy control systems[J]. IEEE Transactions on Automatic Control, 2003, 11(4): 582–589.Google Scholar