Integrated design of fault detection for LTI systems: An iterative LMI approach

In this paper, an integrated design approach of observer based fault detection (FD) for LTI systems is proposed. In the context of norm based residual evaluation, the residual generator and evaluator are designed together in an integrated form with the help of linear matrix inequality (LMI) techniques. The obtained FD systems achieve the best trade-off between fault detection rate (FDR) and false alarm rate (FAR), i.e. for a given FAR the FDR is maximized. A numerical example is given to illustrate the effectiveness of the proposed design approach.