H∞ fuzzy filtering for discrete-time fuzzy stochastic systems with time-varying delay

This paper is concerned with the problem of H_∞ filtering for discrete-time Takagi-Sugeno (T-S) fuzzy Itô stochastic systems with time-varying delay. Attention is focused on the design of a fuzzy-rule-dependent H_∞ filter such that the filter error system is mean-square asymptotically stable and preserves a prescribed noise attenuation level in the H_∞ sense. Delay-dependent criterion is established for the filter error system without ignoring any useful terms in the derivative of Lyapunov functional, which is dependent on the lower and upper delay bounds. The developed theoretical results are expressed in terms of linear matrix inequalities (LMIs) and can be obtained from the solution of a convex optimization problem. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed method.