LMI-Based Unknown Input Observer Design for Fault Detection

In this paper, a new approach is proposed to solve robust fault detection problem using unknown input observer (UIO). Linear matrix inequality (LMI) tool is utilized to design observer gain in the presence of both modeling uncertainty and disturbance. In the proposed method compared to previous approaches, which consider only external disturbances, modeling uncertainty is also considered and the UIO is utilized to detect actuators and sensors fault using residual signal. Moreover, a better solution is proposed to establish disturbance decoupling condition during observer design procedure. Indeed the output matrix of observer, is corrected by one which obtained by LMI. In order to evaluate the ability and performance of the presented method, it is adopted to detect sensor and actuator fault of a linear time invariant (LTI) system in the presence of both model uncertainty and external disturbance. Simulation results show that unknown disturbance is completely decoupled from fault, and a degree of robustness against modeling uncertainty is achieved.