Improved stability and stabilization conditions for Takagi-Sugeno fuzzy systems with time delay

This paper proposes new stability and stabilization conditions for delayed Takagi-Sugeno (T-S) fuzzy systems. For the time delay issue, we use the canonical Bessel-Legendre integral inequality along with an augmented Lyapunov-Krasovskii functional. Therefore, we address the conservatism that arises from the quadratic expression of the augmented Lyapunov-Krasovskii functional by proposing a set of integral functions that include information about the membership functions (MFs) and satisfy the property of a convex set. Based on these functions, we propose an MF-dependent augmented Lyapunov functional that allows us to derive less conservative stability and stabilization conditions for the system and avoid dealing with MFs derivatives. To demonstrate the effectiveness of the proposed strategy, we present simulated results for two examples.