Delay-Distribution-Dependent Robust H∞ Control for T-S Fuzzy Systems with Time-Varying Delay

In this paper, robust H-infinity control for Takagi-Sugeno (T-S) fuzzy system with probabilistic interval time-varying state delay is considered. By considering the probability distribution properties of the time-varying delay taking values between the two given intervals, employing the parallel distributed compensation approach, a new state-space model whose system matrix contains random variables is proposed. Based on the new type of T-S model, resorting to linear matrix inequality (LMI) technique and Lyapunov-Krasovskii functional, the problem of delay-distribution-dependent stability criteria and H-infinity controller synthesis is discussed. An illustrative example is proposed to show the effectiveness and feasibility of the proposed design method and can lead to less conservative result than using the traditional interval time-varying only.