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New robust delay-dependent stability and \(H_{\infty}\) analysis for uncertain Markovian jump systems with time-varying delays. (English) Zbl 1286.93199
Summary: This paper deals with the problems of robust delay-dependent stability and \(H_{\infty}\) analysis for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays. In terms of linear matrix inequalities, an improved delay-range-dependent stability condition for Markovian jump systems is proposed by constructing a novel Lyapunov-Krasovskii functional with the idea of partitioning the time delay, and a sufficient condition is derived from the \(H_{\infty}\) performance. Numerical examples are provided to demonstrate efficiency and reduced conservatism of the results in this paper.

MSC:
93E15 Stochastic stability in control theory
93D09 Robust stability
60J75 Jump processes (MSC2010)
93B36 \(H^\infty\)-control
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