Finite-Time Stabilization of a Class of T–S Fuzzy Systems

Abstract

This paper considers the finite-time stabilization problem for a class of nonlinear systems that can be described by Takagi–Sugeno (T–S) fuzzy models. We propose a novel finite-time switching fuzzy control scheme for T–S fuzzy models, and the scheme is based on the Lyapunov stability theory and the control Lyapunov function technique. It is shown that the finite-time fuzzy controller and the quadratic control Lyapunov function can be obtained at the same time by solving a set of linear matrix inequalities, which can be easily facilitated by available software packages. It is also shown that the potential control law singularity can be avoided with the proposed control scheme. Unlike many existing approaches to finite-time stabilization of general nonlinear systems, the proposed approach does not require the restrictive assumption on the existence of a control Lyapunov function before the corresponding control law is constructed. Furthermore, a finite upper bound on the settling time is estimated, which indicates that within the settling time, the system trajectory would arrive and stay at the origin thereafter. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.