Stability Analysis and Performance Deign for Fuzzy-Model-Based Control System under Imperfect Premise Matching

This paper presents the stability analysis and performance design for nonlinear systems. The T-S fuzzy model is employed to represent the nonlinear plant to facilitate the stability analysis. A fuzzy controller, under imperfect premise matching such that the T-S fuzzy model and the fuzzy controller do not share the same membership functions, is proposed to perform the control task. Consequently, the design flexibility can be enhanced and simple membership functions can be employed to lower the structural complexity of the fuzzy controller. However, the favourable characteristic given by perfect premise matching will vanish, which leads to conservative stability conditions. In this paper, under imperfect premise matching, the information of membership functions of the fuzzy model and controller is considered during the stability analysis. LMI-based stability conditions are derived to guarantee the system stability using the Lyapunov-based approach. Free matrices are introduced to alleviate the conservativeness of the stability conditions. LMI-based performance conditions are also derived to guarantee the system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.