New LMI Approach to Fuzzy $H_{\infty }$ Filter Designs

This brief is concerned with the H _infin filtering problem for a class of discrete-time fuzzy systems. The objective is to find a new way to design a stable filter guaranteeing the asymptotic stability and a prescribed H _infin performance of the filtering error system. By using the fuzzy Lyapunov function approach and adding slack matrix variables, a new condition for H _infin performance analysis is proposed. Then, a linear matrix inequality (LMI)-based approach is developed for designing the fuzzy H _infin filter, which can be obtained from the solution of convex optimization problems. When these LMIs are feasible, an explicit expression of a desired H _infin fuzzy filter is given. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.