Stability Analysis of T-S Fuzzy Systems via Delay-Dependent Lyapunov–Krasovskii Functionals and Linear Switching Method

This paper investigates the problem of stability analysis for Takagi–Sugeno fuzzy systems with time-varying delays. By integrating an augmented delay-dependent Lyapunov–Krasovskii functional (LKF) structure, a refined LKF based on auxiliary function-based integral inequalities, and utilizing a linear switching method, this paper proposes less conservative stability criteria that effectively enhance fuzzy membership characteristics. The proposed stability criteria are formulated in the framework of linear matrix inequalities. Through three numerical examples, the effectiveness and superiority of the proposed approach are demonstrated by achieving significantly improved maximum delay bounds compared to the existing literature.