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This considers the problem of <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance index <inline-formula> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula>. Based on the linear matrix inequalities (LMIS) techniques, the mode-dependent singular matrices <inline-formula> <tex-math notation="LaTeX">$E_{(r_{t})}$ </tex-math></inline-formula> and the stochastic Lyapunov function method, a sufficient condition for the desired <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> controller for the system under consideration is given in terms of LMIs. Moreover, to clarify the proposed results, some illustrative examples are presented.

$H_{\infty}$ Controller Design for Singular Stochastic Markovian Jump System With Time-Varying Delay