Wang, Junru; Wang, Huijiao; Xue, Anke; Lu, Renquan Delay-dependent \(H_{\infty }\) control for singular Markovian jump systems with time delay. (English) Zbl 1257.93032 Nonlinear Anal., Hybrid Syst. 8, 1-12 (2013). 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. Cited in 51 Documents MSC: 93B36 \(H^\infty\)-control 93E03 Stochastic systems in control theory (general) 60J75 Jump processes (MSC2010) 93B12 Variable structure systems Keywords:singular Markovian jump system; \(H_{\infty }\) control; time delay; delay subinterval decomposition approach PDFBibTeX XMLCite \textit{J. Wang} et al., Nonlinear Anal., Hybrid Syst. 8, 1--12 (2013; Zbl 1257.93032) Full Text: DOI