Local stability and stabilization of discrete-time Takagi-Sugeno fuzzy systems using bounded variation rates of the membership functions

Abstract

This paper deals with the problems of local stability analysis, local stabilization, and the computation of invariant subsets of the domain of attraction for discrete-time Takagi-Sugeno fuzzy systems. Fuzzy Lyapunov-based local stability and stabilization conditions are presented by focusing on the case when bounds on variation rates of the membership functions are a priori given. The mean value theorem and polytopic bounds on the gradient of the membership functions are used to consider the relation between membership functions at samples k and k + 1. The conditions are eigenvalue problems, which are solvable via convex optimizations. Examples compare the proposed conditions with existing tests.