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Zbl 1241.34080
Botmart, T.; Niamsup, P.; Phat, V.N.
Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays. (English)
[J] Appl. Math. Comput. 217, No. 21, 8236-8247 (2011). ISSN 0096-3003

The problem of exponential stability and stabilization is studied for a class of uncertain linear systems with time-varying delay. The time delay is a continuous function belonging to a given interval, which means that the lower and the upper bounds for the time-varying delay are available. \par The distinctive features of the presented results are, by the author's opinion, the following: the delay function is not necessary to be differentiable and the lower bound of the delay is not restricted to be zero. Notice that, in the most delay-dependent stability results for systems with time-varying delay, the time delay function is required to be differentiable and, moreover, the upper bound of the derivative is restricted to a number less than unity. \par Based on the construction of some Lyapunov-Krasovskii functionals, new delay-dependent sufficient conditions for the exponential stabilization of the systems are established in terms of LMIs. Numerical examples are given to demonstrate the effectiveness of the derived conditions.
[Nataliya O. Sedova (Ulyanovsk)]

MSC 2000:: *34K20 Stability theory of functional-differential equations
34K06 Linear functional-differential equations
34K27
34K35 Functional-differential equations connected with control problems

Keywords: uncertain linear delay system; time-varying delay; stability; Lyapunov functional; linear matrix inequality

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