An Extension of Tanaka-Sugeno's Stability Theorem for Fuzzy Systems

Abstract

In Tanaka-Sugeno's stability theorem for fuzzy systems, the existence of a symmetric positive definite matrix P satisfying the Lyapunov inequalities plays an important role. The aim of this paper is to propose the P-region method for finding a set of P(2×2), and to generalize it into an extended case P(n×n). Also, a corollary for the theorem is given, and it is shown that for applications of Tanaka-Sugeno's stability theorem to the design of fuzzy control, an extension based on the proposed method and corollary will present a more actual and helpful tool.