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

Abstract 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.

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