Filtering for Discrete-Time Takagi–Sugeno Fuzzy Nonhomogeneous Markov Jump Systems With Quantization Effects

Abstract

This article deals with the problem of H_∞ and l₂-l_∞ filtering for discrete-time Takagi-Sugeno fuzzy nonhomogeneous Markov jump systems with quantization effects, respectively. The time-varying transition probabilities are in a polytope set. To reduce conservativeness, a mode-dependent logarithmic quantizer is considered in this article. Based on the fuzzy-rule-dependent Lyapunov function, sufficient conditions are given such that the filtering error system is stochastically stable and has a prescribed H_∞ or l₂-l_∞ performance index, respectively. Finally, a practical example is provided to illustrate the effectiveness of the proposed fuzzy filter design methods.