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 (LMIs), 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. © 2009 The Franklin Institute.

Hien L.V., Phat V.N.

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Từ khóa : Exponential stability; Lyapunov-Krasovskii functional; Multiple delays; Norm-bounded uncertainty; Numerical example; Robust stability conditions; Time varying; Time-delay system; Uncertain linear time-delay systems; Uncertainty; Convergence of numerical methods; Delay control systems; Linear control systems; Linear matrix inequalities; Switching systems; System stability; Time delay; Time varying systems; Uncertain systems; Stabilization