Stability Analysis of Time-Varying Delay T–S Fuzzy Systems via Quadratic-Delay-Product Method

The stability of Takagi–Sugeno (T–S) fuzzy systems with time-varying delay is investigated in this article. First of all, a novel Lyapunov–Krasovskii functional (LKF) is proposed by fully utilizing single integral polynomial-delay-product terms and membership-function-dependent matrices, where more delay information is considered. Second, by introducing negative integral estimation inequalities and polynomial inequality, the estimation gap of derivatives is further decreased. As consequence, the criterion with less conservatism is presented. Finally, the examples are utilized for verifying the validity of the stability approach.