A novel method for fault detection in singularly perturbed systems via the finite frequency strategy

This paper addresses the fault detection synthesis for a class of linear singularly perturbed systems with unknown disturbances. The observer is designed via a novel method, in which singularly perturbed systems could be processed within a uniform framework instead of using the classical slow-fast decomposition. The problem of robust fault detection can be converted into a standard H∞ model-matching. Based on the generalized Kalman-Yakubovich-Popov lemma and parameter-dependent Lyapunov functions, a full-order observer is designed such that the corresponding error dynamic system is asymptotically stable and satisfies a prescribed finite-frequency H_/H∞ performance index. A novel three-step design procedure is then proposed to extract the fault feature from strong background disturbances. An illustrative example is given to demonstrate the validity and applicability of the proposed approaches in the simulation part.