Non-fragile H∞ filter design for discrete-time fuzzy systems with multiplicative gain variations

This paper investigates the problem of non-fragile H∞ filter design for discrete-time Takagi–Sugeno (T–S) fuzzy systems. The filter to be designed is assumed to have two type of multiplicative gain variations. By introducing additional matrix variables, a relaxed H∞ filtering analysis criterion is presented for the fuzzy system based on the fuzzy Lyapunov function. A filter state transformation approach is adopted to design the non-fragile H∞ filter, and the filter gains are given in terms of the feasible solutions of a set of linear matrix inequalities (LMIs). A simulation example is given to show the efficiency of the proposed methods.