Harnessing Membership Function Dynamics for Stability Analysis of T-S Fuzzy Systems

The main goal of this paper is to develop a new linear matrix inequality(LMI) condition for the asymptotic stability of continuous-time Takagi-Sugeno(T-S) fuzzy systems. A key advantage of this new condition is its independencefrom the bounds on the time-derivatives of the membership functions, arequirement present in the existing approaches. This is achieved by introducinga novel fuzzy Lyapunov function that incorporates an augmented state vector.Notably, this augmented state vector encompasses the membership functions,allowing the dynamics of these functions to be integrated into the proposedcondition. This inclusion of additional information about the membershipfunction serves to reduce the conservativeness of the suggested stabilitycondition. To demonstrate the effectiveness of the proposed method, examplesare provided.