< Inline-Formula > < Tex-Math Notation="Latex">$H_{\Infty}$ Controller Design For Singular Stochastic Markovian Jump System With Time-Varying Delay

This considers the problem of $H_{\infty }$ controller design for singular stochastic systems. The systems have Markovian jump and time-varying delay. We aim to design a controller ensuring the closed-loop system is stochastically admissible and satisfies a prescribed $H_{\infty }$ performance index $\gamma $ . Based on the linear matrix inequalities (LMIS) techniques, the mode-dependent singular matrices $E_{(r_{t})}$ and the stochastic Lyapunov function method, a sufficient condition for the desired $H_{\infty }$ controller for the system under consideration is given in terms of LMIs. Moreover, to clarify the proposed results, some illustrative examples are presented.