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In this paper, we focus on discussing the delay-dependent dissipative filtering problem for a type of singular time-varying delay systems with random disturbance. At first, we construct a proper candidate Lyapunov-Krasovskii functional, then on the basis of an auxiliary vector function and the free weighting matrix technique, the stochastic admissibility and stochastic dissipation conditions for the considered filtering error system are derived. Furthermore, the corresponding filter design method is then proposed. In addition, we address the solving approach for the <inline-formula> <tex-math notation="LaTeX">${\mathrm {H}}_\infty $ </tex-math></inline-formula> filtering as a special case of dissipative filtering. The sufficient conditions are derived guaranteeing the stochastic admissibility for the filtering error system consideration, and achieving a prescribed performance index <inline-formula> <tex-math notation="LaTeX">$\hat {\gamma }$ </tex-math></inline-formula>. At last, a numerical example is given to demonstrate the effectiveness of our proposed filter design method in the paper.

Dissipative Filtering for Stochastic Singular Time-Varying Delay Systems