Design of fault estimator for singular fractional‐order systems in finite frequency domain

This paper addresses the problem of finite‐frequency fault estimation for singular fractional‐order systems (FOS). The two performance indices of singular FOS are utilized to measure unknown disturbances and finite frequency domain faults. A nonsingular fault estimator is proposed, which is easy to implement. Robust design conditions for fault estimators are provided via a set of linear matrix inequalities (LMIs) to mitigate the effects of unknown disturbances and finite frequency domain faults based on the generalized Kalman–Yakubovich–Popov (GKYP) lemma. In contrast to existing full‐frequency methods, the finite frequency domain approach proposed in this paper significantly enhances the accuracy of fault estimation. Finally, a simulation example is presented to validate the effectiveness of the proposed method.