Robust H∞ adaptive descriptor observer design for fault estimation of uncertain nonlinear systems

This paper proposes a novel fault estimation observer for both nonlinear descriptor and normal systems, which are subjected simultaneously to actuator faults, sensor faults and unstructured non-parametric uncertainties. The considered faults can be unbounded and can have many forms, such as abrupt faults, constant faults and high-frequency faults. Sufficient conditions for the existence of the proposed observer with an H∞ performance have been derived based on Lyapunov stability theory, and expressed in terms of Bilinear Matrix Inequalities (BMIs) which are then converted into quasi-convex Linear Matrix Inequalities (LMIs) by using the cone complementarity linearization (CCL) algorithm. Simulated examples are presented to illustrate the effectiveness of the proposed observer for both descriptor systems and normal systems and have been shown to perform better than some of the existing methods of fault estimation.