Fault Estimation Based on an Adaptive Observer for a Class of Uncertain Nonlinear Descriptor Systems

First, an H-infinity adaptive observer is designed for a class of uncertain nonlinear descriptor systems. This observer can simultaneously estimate the actuator faults, sensor faults, and system states in the presence of uncertainty and output disturbance. Various types of faults, such as abrupt faults and incipient faults, can be estimated using the observer. Then, the observer is designed without requiring some conditions to be satisfied. The observer stability is analyzed using the Lyapunov stability theory. Then, the sufficient conditions for the existence of the observer are converted into linear matrix inequalities (LMIs). The proposed method does not need the Lipschitz constant in the LMI formulation. Therefore, the proposed method can be applied to systems with unknown or large Lipschitz constants. Additionally, unlike the conventional adaptive estimator, the proposed estimator has both proportional and integral components to enhance the accuracy and rapidity of the estimation. Two simulation examples are provided to illustrate the effectiveness of the proposed method for descriptor systems and normal state-space systems.