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Delay-dependent \(H_{\infty }\) control for singular Markovian jump systems with time delay. (English) Zbl 1257.93032

Summary: This paper deals with the problem of delay-dependent \(H_{\infty }\) control for singular Markovian jump systems with time delay. Based on the delay subinterval decomposition approach, a new Lyapunov-Krasovskii functional is proposed to develop the new delay-dependent Bounded Real Lemma (BRL), which ensures the considered system to be regular, impulse-free and stochastically stable with given \(H_{\infty }\) performance index \(\gamma \). Based on this new BRL, the explicit expression of the desired controller gains is also presented by solving a set of strict LMIs. Some numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

MSC:

93B36 \(H^\infty\)-control
93E03 Stochastic systems in control theory (general)
60J75 Jump processes (MSC2010)
93B12 Variable structure systems
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