Regional Stabilization and Estimation of Domains of Attraction for Discrete-Time T-S Fuzzy Systems via Fuzzy-modeled Membership Functions

Abstract

This article addresses the problem of regional stabilization for discrete-time Takagi-Sugeno fuzzy systems using parallel distributed compensation output-feedback controllers. The goal is to ensure asymptotic stability and to maximize the estimate of the corresponding domain of attraction. The key contribution of this work is the use of a fuzzy modeling approach for the membership functions, enabling a polytopic representation based on the premise variables. Unlike conventional approaches, this method avoids the need for explicit bounds on membership function variations, thereby reducing conservatism in the stabilization conditions. The synthesis procedure is presented as an iterative algorithm based on linear matrix inequalities, consisting of two distinct phases: the first phase stabilizes the system, while the second phase aims to maximize the estimated region of attraction. Numerical examples are provided to demonstrate the advantages of the proposed technique over existing methods.