Membership-function-dependent stability analysis of fuzzy-model-based control systems using fuzzy Lyapunov functions

This paper investigates the stability of fuzzy-model-based (FMB) control system, formed by a T–S fuzzy model and a fuzzy controller connected in a close loop, based on a fuzzy-Lyapunov function. A general FMB control system that the T–S fuzzy model and fuzzy controller not sharing the same premise membership functions and/or the same number of fuzzy rules is considered. A membership-function-dependent stability analysis approach is proposed to consider the membership functions of both the T–S fuzzy model and fuzzy controller in the stability analysis and incorporate them in the stability conditions in the form of linear matrix inequalities. As the stability conditions are membership-function dependent, they are dedicated to the FMB control system with the specified membership functions under consideration. It is thus the membership-function-dependent stability conditions are more relaxed compared to the existing membership-function-independent stability conditions. A fuzzy-Lyapunov function is a weighted sum of quadratic functions which are required to be positive definite in most of the existing work. In this paper, this criterion is not required and thus the stability conditions can be further relaxed. Some simulation examples are given to demonstrate the merits of the proposed approach.