Local stability analysis of T-S fuzzy systems using second-order time derivative of the membership functions

This paper addresses the local stability analysis problem for continuous-time Takagi–Sugeno (T–S) fuzzy systems. Based on the Lyapunov method, the proposed analysis procedure is formulated as optimizations subject to linear matrix inequalities (LMIs) which can be solved by means of convex optimization techniques. Especially, a generalized Lyapunov function that depends on the membership functions (MFs) and its time derivatives is used. Since the Lyapunov function involves the time derivatives of the MFs, the problem of stability analysis and the estimation of the domain of attraction (DA) cannot be converted into convex problems in general. In this paper, we explore the possibility of using the second-order time derivatives of the MFs to determine the DA. Examples are given to illustrate the proposed method.