An investigation of set-theoretic methods for fault detection in Lure systems

A recently proposed set-theoretic approach to fault diagnosis is based on membership of residual signals to (invariant) sets that characterise healthy and faulty system behaviour. Correct diagnosis is achieved if the relevant sets are disjoint. Tighter sets that allow separation for a larger class of faults are hence desirable within this approach. In this paper, we investigate methods to compute invariant sets for a Lure system from two different perspectives: by bounding the nonlinear terms and by embedding the nonlinear system in a linear parameter varying (LPV) model. To analyse and compare the methods, we develop a scalar and a second-order system case, and provide an example of a latter system. The results show that both approaches can be used for fault diagnosis and yield comparable performance for this type of systems under specific conditions.