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Exponential stability and stabilization of a class of uncertain linear time-delay systems. (English) Zbl 1169.93396
Summary: This paper presents new exponential stability and stabilization conditions for a class of uncertain linear time-delay systems. The unknown norm-bounded uncertainties and the delays are time-varying. Based on an improved Lyapunov-Krasovskii functional combined with Leibniz-Newton formula, the robust stability conditions are derived in terms of linear matrix inequalities, which allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. The result can be extended to uncertain systems with time-varying multiple delays. The effectiveness of the two stability bounds and the reduced conservatism of the conditions are shown by numerical examples.

MSC:
93D21 Adaptive or robust stabilization
93C05 Linear systems in control theory
93C41 Control/observation systems with incomplete information
34D99 Stability theory for ordinary differential equations
93D09 Robust stability
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