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

This considers the problem of H
_∞
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
_∞
performance index γ. 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
_∞
controller for the system under consideration is given in terms of LMIs. Moreover, to clarify the proposed results, some illustrative examples are presented.