Linear matrix inequalities‐based membership‐function‐dependent stability analysis for non‐parallel distributed compensation fuzzy‐model‐based control systems

Abstract

This study investigates the stability of fuzzy-model-based (FMB) control system, which is formed by a Takagi–Sugeno (T–S) fuzzy model representing a non-linear plant and a fuzzy controller connected in a closed loop. The proposed fuzzy controller considers a higher design flexibility that the premise membership functions and the number of fuzzy rules are allowed to be not the same as those of the T–S fuzzy model. By employing simple membership functions and a smaller number of fuzzy rules, the complexity of the fuzzy controller can be reduced to facilitate its implementation. Based on the Lyapunov stability theory, a membership-function-dependent (MFD) stability analysis is proposed to develop stability conditions in the form of linear matrix inequalities (LMIs) to determine the system stability and facilitate the control synthesis. The information of the membership functions is brought to the MFD LMI-based stability conditions, which are dedicated to the FMB control system under consideration. It is thus the proposed MFD stability analysis result is more relaxed compared with the existing membership-function-independent stability analysis results. A simulation example is given to illustrate the effectiveness of the proposed approach.