Fault estimation for fractional-order linear systems with polytopic uncertainties in the finite frequency domain

This paper investigates the problem of fault estimation for fractional-order systems with polytopic uncertainties. The faults and disturbances are considered to belong to finite frequency domains, and a fractional-order robust fault estimation filter is proposed for fault estimation with the known frequency ranges. As applications of the generalized Kalman-Yakubovich-Popov lemma, the fault estimation filter design problem is transformed into a multi-objective optimisation problem. By using the projection lemma and a linearising change of variables, sufficient conditions for the existence of the robust fault estimator are derived on the basis of a set of linear matrix inequalities. Numerical examples are used to demonstrate the validity of the presented method.