Estimation of actuator and sensor faults for nonlinear systems using a descriptor system approach

This paper addresses the problem of simultaneously estimating actuator and sensor faults of Lipschitz nonlinear systems with non-parametric uncertainties. The proposed fault estimation scheme initially takes sensor faults as auxiliary states and an augmented descriptor system is constructed. By designing a modified proportional and derivative (PD) observer with an adaptive law for this system, the estimation of the original system states, sensor faults and actuator faults can be obtained simultaneously. The sufficient condition for stability of the proposed observer with ℋ_∞ performance has been derived based on Lyapunov theory. The stability condition is expressed as Linear Matrix Inequality (LMI) optimization problem for minimizing the ℋ_∞ norm of transfer matrix between the estimation error and uncertainties, which outlines a constructive design procedure for observer parameters. It is shown from the simulation that the proposed approach is capable of successfully estimating states and faults not only for nonlinear state-space systems, but also for nonlinear descriptor systems.