Harnessing Membership Function Dynamics for Local Stability Analysis and Estimation of Domains of Attraction for Discrete-Time T-S Fuzzy Systems

This paper investigates the stability analysis of discrete-time Takagi-Sugeno fuzzy systems by incorporating the dynamics of membership functions (MFs) into an augmented state vector. Using a polytopic representation for the MFs, a novel Lyapunov function that enables the derivation of less conservative linear matrix inequality-based stability conditions is proposed. Unlike existing approaches, the proposed method eliminates the need for predefined MF variation bounds, leveraging their inherent dynamics to refine stability analysis and domain of attraction (DOA) estimation. Numerical examples demonstrate the effectiveness of the proposed approach in reducing conservatism and enlarging the estimated DOA compared to existing methods.