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

This paper is concerned with the stability analysis for Takagi-Sugeno (T-S) fuzzy control systems. By exploiting the property of the structure of a fuzzy inference engine, an equivalence relation on the index set of the product of fuzzy rule weights is defined. Furthermore, 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..