Delay-dependent dissipative filtering for nonlinear stochastic singular systems with time-varying delays

Abstract

This paper concentrates on studying the delay-dependent dissipative filtering problem for nonlinear stochastic singular systems with time-varying delays via a Takagi-Sugeno (T-S) fuzzy control approach. The T-S fuzzy model is employed to represent a nonlinear stochastic singular system with unknown or partially unknown membership functions. Firstly, based on an auxiliary vector function, by utilizing an integral inequality and the free-weighting-matrix approach, a delay-dependent sufficient condition is derived to enable the considered filtering error system with time-varying delays to be stochastically admissible and dissipative. Furthermore, on the basis of the derived condition, by using a new type of candidate Lyapunov-Krasovskii function, the solvability conditions of the dissipative filter are addressed, and the corresponding fuzzy filter parameters can be obtained by solving a set of linear matrix inequalities. And then, we deduce the solving method for the ${\mathrm{H}}_\infty$ filter. The delay-dependent sufficient conditions are proposed to guarantee the systems to be regular, impulse-free, stochastically stable and to achieve a prescribed performance index $\hat{\gamma}$. Finally, some simulation examples are proposed to manifest the effectiveness and merits of the filter design methodology developed in the paper.