Homogenous Polynomially Parameter-Dependent $H_{ \infty }$ Filter Designs of Discrete-Time Fuzzy Systems

This paper proposes a novel H_∞ filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H_∞ filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H_∞ performance of the filtering error system. Second, relaxed conditions for H_∞ performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H_∞ filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.