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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.

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