Exponential stabilization of fuzzy systems with perturbations by using state estimation

Abstract

In this paper, the concept of practical output feedback controller for Takagi-Sugeno fuzzy models is introduced. Some new sufficient conditions are obtained to ensure the exponential stability using state estimation of the fuzzy control systems in presence of perturbations. We show that all state trajectories of the closed-loop fuzzy system are bounded and approach a sufficiently small neighborhood of the origin. First we consider the stability with state feedback fuzzy controllers and a natural form of observers for the considered models is designed where some restrictions are imposed on the perturbations for their practical exponential convergence. We then show that the state feedback controller and the observer always yield a stabilizing output feedback controller provided that the stabilizing property of the control and the asymptotic convergence of the observer are guaranteed by the Lyapunov method using positive definite matrices. In this sense, it is shown that the separation principle holds, the challenges are discussed and some analysis oriented tools are provided. An example in dimensional two is given to show the effectiveness of the proposed fuzzy-observer-based control approach.