Fault Detection for Lipschitz Nonlinear Systems Using Robust Observer and Ellipsoidal Analysis

This article proposes a fault detection method for continuous-time Lipschitz nonlinear systems via robust observer design and ellipsoidal analysis. First, an augmented system is established by considering the fault as an auxiliary state vector. Then, an observer is designed using $L_{\infty }$ performance, which can be applied to generate robust residuals. Then, a residual evaluation method via ellipsoidal analysis is proposed, which is used to check whether the guaranteed estimations of the fault and residual stay confined inside safe regions. Thus, fault detection is achieved through an assessment of a Boolean expression. Finally, two numerical simulation results are given to show the effectiveness and merit of the proposed approach.