Iterative LMI approach for robust fault detection observer design

This paper deals with the robust fault detection (RPD) problem with the aid of the H_∞ norm and H_ index optimization technique and the LMI approach. A necessary and sufficient condition is proposed for the design of RFD observers. RFD problem with structured uncertainties in the system matrices is also considered. Iterative LMI algorithms are proposed to design RFD observers to enhance the fault detection and to attenuate the effects due to unknown inputs and uncertainties. We also consider the RFD problem over finite frequency range in which case no full column rank constraint is required on D for a system (A, B, C, D). A numerical example is employed to demonstrate the effectiveness of the proposed methods.