## 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
Full Text: