Fault Detection for Discrete-Time Interval Type-2 Takagi–Sugeno Fuzzy Systems Using $H_{-}/L_{\infty }$ Unknown Input Observer and Zonotopic Analysis

For complex nonlinear systems, interval type-2 fuzzy set is a useful strategy due to its ability to deal well with uncertainties in the system, while posing some difficulties to fault detection, such as precise threshold design and fault sensitivity requirements. This article focuses on the fault detection problem of interval type-2 Takagi–Sugeno fuzzy systems with external disturbances, and noises by investigating set-membership estimation. The existing set-membership techniques give the admissible compact set of residuals under the condition of no fault, which is generated by Luenberger-like observer. The boundary of the compact set is affected by the disturbances and noises in the process channel and the measure channel, which results the main difficulty in improving the accuracy of fault detection. To this end, a zonotopic analysis-based $H_{-}/L_{\infty }$ fuzzy fault detection unknown input observer is proposed to decouple disturbances from residual dynamic, to improve the efficiency of fault detection and to further reduce the admissible compact set of residuals. Meanwhile, the Lyapunov function of fuzzy basis dependence is used to analyze the stability and $H_{-}/L_{\infty }$ performance of fault detection unknown input observer, further reducing conservatism. Finally, a simulation example is given to verify the feasibility and effectiveness of the proposed fault detection unknown input observer.