Robust Fault Detection of Uncertain Lipschitz Nonlinear Systems with Simultaneous Disturbance Attenuation Level and Enhanced Fault Sensitivity and Lipschitz Constant

In this paper, the problem of optimal robust fault detection (FD) for uncertain Lipschitz nonlinear systems is considered. A robust active fault detection approach for a class of the Lipschitz nonlinear systems in the presence of disturbances and parametric uncertainties is proposed, wherein the Lipschitz constant is assumed as one of the optimization parameters in the observer design. In addition to disturbance attenuation level, the fault sensitivity criterion based on \(H_-\) index is also defined in the FD system design. Different criteria are defined as a weighted multi-objective linear matrix inequality optimization problem, and the optimal variables of the FD system are derived based on a newly defined cost function. A numerical example is provided to demonstrate the effectiveness of the proposed FD system. The results show the robustness of the proposed method against parametric uncertainty and nonlinear uncertainty as well.