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

This paper proposes a novel <i>H</i>_∞ filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy <i>H</i>_∞ filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed <i>H</i>_∞ performance of the filtering error system. Second, relaxed conditions for <i>H</i>_∞ 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 <i>H</i>_∞ filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.