Dissipative Filtering for Stochastic Singular Time-Varying Delay Systems

Abstract

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 H∞ 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 γ̂. At last, a numerical example is given to demonstrate the effectiveness of our proposed filter design method in the paper.

Keywords

• Stochastic admissibility
• dissipative filtering
• time-varying delays
• H∞ filtering