Robust $H_{\infty }$ Control for T–S Fuzzy Systems With State and Input Time-Varying Delays via Delay-Product-Type Functional Method

This paper investigates the problem of robust H
_∞
control for a class of nonlinear systems with state and input time-varying delays. The nonlinearity is presented by a continuous-time Takagi-Sugeno (T-S) fuzzy model with parameter uncertainties. A sufficient asymptotic stability condition is first proposed by constructing a delay-product-type augmented Lyapunov-Krasovskii functional and utilizing an extended reciprocally convex matrix inequality together with a Wirtinger-based integral inequality. Then, a state feedback controller is derived that guarantees the closed-loop fuzzy system being asymptotically stable with an H
_∞
performance index. Finally, four numerical examples are given to reveal the effectiveness and merits of the developed new design techniques.