Fuzzy filtering of nonlinear fuzzy stochastic systems with time-varying delay

This paper is concerned with the H∞H∞ filtering problem for nonlinear stochastic Takagi–Sugeno (T–S) fuzzy systems with time-varying delay, where the nonlinearities are assumed to satisfy global Lipschitz conditions. Attention is focused on the design of both the fuzzy-rule-independent and the fuzzy-rule-dependent filters that guarantee a prescribed noise attenuation level in an H∞H∞ sense. To reduce the conservatism, a delay-dependent approach developed to derive the main results in terms of linear matrix inequalities (LMIs). When the fuzzy-rule-independent filter is applied, a sufficient condition is first proposed to ensure that the filtering error system is stochastically stable with an H∞H∞ performance. The corresponding solvability condition for a desired fuzzy-rule-independent filter is established by casting the fuzzy-rule-independent filter design into a convex optimization problem. Then, the parallel results are obtained for the case when the fuzzy-rule-dependent filter is used, and these results have less conservatism than those for the fuzzy-rule-independent filter design case. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.