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Stability and \(L_{2}\)-gain analysis for switched delay systems: a delay-dependent method. (English) Zbl 1114.93086
Summary: In this paper, we study stability and \(L_{2}\)-gain for a class of switched systems with time-varying delays. Sufficient conditions for exponential stability and weighted \(L_{2}\)-gain are developed for a class of switching signals with average dwell time. These conditions are delay-dependent and are given in the form of linear matrix inequalities (LMIs). As a special case of such switching signals, we can obtain exponential stability and normal \(L_{2}\)-gain under arbitrary switching signals. The state decay estimate is explicitly given. Two examples illustrate the effectiveness and applicability of the proposed method.

93D20 Asymptotic stability in control theory
93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
Full Text: DOI
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