$H_{-}/L_{\infty }$ Time-Delay Unknown Input Actuator Fault Detection Observer for Discrete-Time Takagi–Sugeno Fuzzy Singular Systems and Zonotopic Residual Analysis

This article focuses on the issue of time-delay unknown input actuator fault detection (FD) observer design dedicated to the discrete-time Takagi–Sugeno fuzzy singular system. Based on the given <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{\infty }$</tex-math></inline-formula> performance and finite-frequency <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{-}$</tex-math></inline-formula> indexes, the observer is established to construct the residuals that are robust against disturbances and sensitive to actuator faults simultaneously. Under the assumption that disturbances are unknown but bounded, according to the set-membership techniques, all FD thresholds generated by fault-free residuals are propagated in a sequence of zonotopes. Moreover, compared with existing unknown input observers, the designed observer overcomes the issue of incomplete decoupling between residuals and unknown disturbances, thereby reducing the conservatism in FD. Furthermore, by introducing arbitrary matrices and relaxation matrices, the originally nonconvex observer design conditions are transformed into a minimization optimization problem under linear matrix inequalities. The tradeoff between robustness to disturbances and sensitivity to faults can be achieved by the iterative solution algorithm, contributing to less conservatism and satisfactory FD performance. The effectiveness of the proposed FD strategy is validated by simulations based on a truck–trailer dynamic model.