H_∞ fuzzy filtering for discrete-time nonlinear systems via fuzzy Lyapunov function approach

This paper is concerned with the H_∞ fuzzy filtering problem for a class of discrete-time fuzzy systems. The objective is to design a stable filter guaranteeing the asymptotic stability and a prescribed H_∞ performance of the filtering error system. Motivated by the parallel distributed compensation (PDC) technique, a new filter model is proposed in this paper. Both full-order and reduced-order filters are established, and they can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H_∞ fuzzy filter is given. A numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.