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Robust stability and \(H_\infty\) stabilization of switched systems with time-varying delays using delta operator approach. (English) Zbl 1296.93160

Summary: This paper considers the problems of the robust stability and robust \(H_\infty\) controller design for time-varying delay switched systems using delta operator approach. Based on the average dwell time approach and delta operator theory, a sufficient condition of the robust exponential stability is presented by choosing an appropriate Lyapunov-Krasovskii functional candidate. Then, a state feedback controller is designed such that the resulting closed-loop system is exponentially stable with a guaranteed \(H_\infty\) performance. The obtained results are formulated in the form of linear matrix inequalities (LMIs). Finally, a numerical example is provided to explicitly illustrate the feasibility and effectiveness of the proposed method.

MSC:

93D09 Robust stability
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