$H_{-}/L_{\infty }$ Fault Detection Observer Design for Uncertain Lipschitz Nonlinear Systems

This paper deals with the robust fault detection problem in the finite frequency domain for a class of Lipschitz nonlinear systems with uncertain parameters. The design conditions of $H_{-}/L_{\infty }$ fault detection observers are proposed. These conditions make the error estimation system stable, and the residual has $L_{\infty }$ disturbance attenuation performance for external disturbances and uncertain parameters. In addition, considering that fault occurs in the finite frequency domain, the residual also has $H_{-}$ fault sensitivity performance. To ease of solution, the observer design conditions are further transformed into linear matrix inequalities. On this basis, a dynamic threshold design method based on $L_{\infty }$ analysis is presented. Finally, simulation results demonstrate the superiority of the proposed method.