Interval-Observer-Based Zonotopic Residual Fault Detection and Isolation for Lipschitz Nonlinear T-S Fuzzy Systems

This paper addresses the fault detection and isolation (FDI) problem for discrete-time Lipschitz nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. A zonotopic set-membership estimation framework is proposed to robustly handle system uncertainties and bounded disturbances. First, an$H_\infty$observer is designed based on linear matrix inequality (LMI) conditions to ensure robust performance. The estimation error is bounded within a recursively propagated zonotope, where generator growth is controlled via zonotope order reduction. Second, a fault detection scheme is developed by constructing residual zonotopes and checking whether the residual lies within the associated bounding boxes. Third, to achieve fault isolation, two augmented observers are designed, respectively addressing actuator fault isolation and sensor fault isolation. For actuator fault isolation, a state-augmented observer is proposed to eliminate the influence of sensor faults in the residual. For sensor fault isolation, a disturbance-augmented observer is constructed to decouple the actuator fault effect. In both cases, zonotopic residual bounds are derived to detect and isolate the fault source. Finally, simulation results on a fuzzy nonlinear system illustrate the effectiveness and robustness of the proposed fault detection and isolation approach.