Stability Analysis of T-S Fuzzy Control Systems by Using Set Theory

This paper is concerned with the stability analysis for T-S fuzzy control systems. By exploiting the property of the structure of fuzzy inference engine, an equivalence relation on index set of the product of fuzzy rule weights is defined. Further, a new stability criterion is proposed by using the equivalence relation, and formulated into progressively less conservative sets of linear matrix inequalities. By using an extension of Pólya’s Theorem, the new criterion is proved to be with no conservatism for quadratic stability analysis of T-S fuzzy control systems with a product inference engine and any possible fuzzy membership functions. A numerical example is given to illustrate the effectiveness of the proposed method.