Robust fault estimation for singularly perturbed systems with Lipschitz nonlinearity

In this paper, observer-based fault estimation problem is addressed for Lipschitz nonlinear singularly perturbed systems with respect to sensor faults. A robust fault estimation scheme is presented to estimate faults whose derivative is bounded. With this method, the proposed fault estimator minimizes the effect of uncertainty on the estimation error and maximizes stability bound of the system simultaneously. To be specific, a sufficient condition for existence of the proposed fault estimator is firstly derived in the form of LMIs. This condition enables the fault estimator to be robust to uncertainty in terms of a prescribed H∞ performance index. Then, the largest stability bound and the best uncertainty attenuation capacity are guaranteed by deriving a modified multi-objective optimal algorithm. An armature-controlled DC motor example is finally given to illustrate the effectiveness of the proposed scheme.