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		Nam PHAN T.,Phat VU N..[en_title][J].Control Theory and Technology,2008,6(2):163~170.[Copy]

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NamPHANT.,PhatVUN.
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Received:June 15, 2006Revised:July 19, 2007

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Robust exponential stability and stabilization of linear uncertain polytopic time-delay systems

Nam PHAN T., Phat VU N.

(Department of Mathematics, Quynhon University, Quynhon, Binhdinh, Vietnam; Institute of Mathematics, 18 Hoang Quoc Viet Road, Hanoi, Vietnam)

Abstract:

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 exponetial stability rate of the solution. Numerical examples illustrating the conditions are given.

Key words: Polytopic time-delay system Exponential stability Stabilization Parameter-dependent Lyapunov function Linear matrix inequalities