Fault Detection for Lipschitz Nonlinear Systems With Restricted Frequency-Domain Specifications

This article deals with the problem of fault detection for discrete-time Lipschitz nonlinear systems subject to a class of restricted frequency-domain specifications. We present a novel observer structure with more design parameters, which can be applied to enhance the observer performance. The performances of fault sensitivity and disturbance robustness are characterized using finite-frequency $H_{-}$ and $H_{\infty }$ indices, respectively. Less restrictive design conditions are obtained based on a reformulated Lipschitz property. Moreover, to detect faults timely, a novel dynamic threshold is synthesized based on zonotopic set-membership techniques. Simulation examples are conducted to demonstrate the viability and validity of the presented method.