Robust fast adaptive fault estimation and tolerant control for T-S fuzzy systems with interval time-varying delay

This paper studies the problem of fault estimation (FE) and the active fault tolerant control (FTC) for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay and norm-bounded external disturbance. Based on the fast adaptive fault estimation (FAFE) algorithm, our attention focuses on designing an adaptive observer-based controller to guarantee the filtering error system to be asymptotically stable and satisfy the H-infinity performance index. By constructing a new Lyapunov-Krasovskii functional including the information of the lower and upper delay bounds, the sufficient delay-dependent conditions have been established to guarantee the existence of adaptive observer-based controller in terms of linear matrix inequalities (LMIs). Compared with the constant delay and time-varying delay, the interval time-varying delay is the less conservative form. Furthermore, we make full use of the information of the delay and no terms are ignored when the stability of the system is analysed. In addition, the results for the systems with time-varying structured uncertainties are established. The results of the active FTC are showed in terms of LMIs. Finally, two examples are given to verify the effectiveness of the proposed method.