A new relaxed stability condition for Takagi-Sugeno fuzzy control systems using quadratic fuzzy Lyapunov functions and staircase membership functions

This paper presents a new relaxed stability condition for Takagi-Sugeno (T-S) fuzzy control systems. Using quadratic fuzzy Lyapunov functions (QFLFs), the stability of closed-loop control system is guaranteed by the negative definiteness of several fuzzy summations. However, since the membership functions are continuous, the negative definiteness of these fuzzy summations implies an infinite number of linear matrix inequalities (LMIs), which cannot be solved directly by conventional convex optimization methods. To handle this problem, Staircase Membership Functions (SMFs) are employed to convert the infinite number of LMIs into a finite one. At the same time, the information of membership functions is brought into stability analysis, which substantially relaxes the proposed stability condition. The efficiency of the presented approach is demonstrated by using two simulation examples.