Fault detection for fractional‐order linear systems in finite frequency domains

Abstract

This study is concerned with the fault detection problem for fractional-order linear systems with disturbances. The H − and H ∞ performance indices of fractional-order systems in finite frequency domains are applied to measure the fault sensitivity and the disturbance robustness. A fractional-order fault detection observer is designed to satisfy the two finite frequency performance indices simultaneously. Based on the generalised Kalman–Yakubovich–Popov lemma and the projection lemma, the design conditions are obtained in terms of linear matrix inequalities. Compared with the existing full frequency approaches, the proposed finite frequency one can get better results when the frequency ranges of faults and disturbances are known. The effectiveness of the proposed method is validated by numerical examples.