Fault Estimations for Uncertain Linear Discrete-time Systems in Low Frequency Domain

This paper studies the problem of fault estimations for linear time-invariant discrete-time systems with polytopic uncertainties. Generalized Kalman-Yakubovich-Popov (GKYP) lemma is exploited to formulate the fault detection (FD) filter design problem in low frequency domain. The filter is designed to make the error between residual and fault as small as possible. A design method is presented in terms of solutions to a set of linear matrix inequalities(LMIs). A numerical example is given to illustrate the effectiveness of the proposed method.