Robust Observer-Based Fault Estimation for Lipschitz Nonlinear Systems with State-Coupled Disturbance: A Dissipativity Approach

Abstract

In this paper, a robust fault diagnosis method is proposed to estimate the states and faults simultaneously for a special class of Lipschitz nonlinear systems. In the model of system, fault is considered as a linear and additive function and disturbance as a nonlinear function coupled with the system states. An augmented system is constructed by forming a vector composed of states and faults, and a Luenberger observer is designed for fault estimation. The nonlinear function of state-coupled disturbance is replaced by a Lipschitz matrix. In order to reduce the conservatism of the problem, this matrix depends on both the states and disturbances. This approach attempts to attenuate the effects of the state-coupled disturbances using the dissipativity theory such that the existing problem finally leads to solving convex optimization problems. The necessary conditions for the existence of such an observer are expressed. Finally the performance of the proposed method is simulated on a robot, and the results indicate good performance of the proposed method.