Robust Fault Detection Observer Design: Iterative LMI Approaches

This paper deals with the Robust Fault Detection (RFD) problem with the aid of the H∞ norm and H− index optimization techniques and the LMI approach. First, a necessary and sufficient condition is proposed for the design of RFD observers in the nominal case. Then, the RFD problem for systems with structured uncertainties in the system matrices is considered. Approaches are proposed to design robust fault detection observers to enhance the fault detection and to attenuate the effects due to unknown inputs and uncertainties. Furthermore, the design of the threshold of fault detection is investigated. We also consider the fault sensitivity over finite frequency range in which case no constraint is required on D being of full column rank for a system (A,B,C,D). Numerical examples are employed to demonstrate the effectiveness of the proposed methods.