Delay-dependent H∞ filtering for discrete-time fuzzy stochastic systems with mixed delays and sector-bounded nonlinearity

The delay-dependent H∞ filter problem for discrete-time Takagi-Sugeno (T-S) fuzzy stochastic systems with mixed delays and sector-bounded nonlinearity is considered in this paper. The mixed delays consist of both discrete and distributed delays, and the nonlinearity under consideration is subject to sector-bounded condition. Both the the fuzzy-rule-dependent and fuzzy-rule-independent filters are considered. Based on discrete Jensen inequality and the Lyapunov-Krasovskii functional approach combined with the S-procedure, sufficient conditions for the existence of admissible filters are established in terms of linear matrix inequalities (LMIs), which ensure the asymptotical mean-square stability as well as a prescribed H∞ performance. Finally, numerical examples are given to demonstrate the effectiveness and less conservatism of the proposed approach.