A relaxed LMI approach to actuator fault detection and isolation

This paper presents an intuitive Fault Detection and Isolation (FDI) synthesis method for linear time invariant systems subject to faults. The proposed method uses the notion of ultimate boundedness to relax certain feasibility conditions, meaning that the resulting problem can be posed in a similar manner to an intuitive H-infinity minimization problem. It is then possible to show, using a quadratic Lyapunov function, that the error states are bounded - rather than they converge asymptotically to zero - and that minimizing a certain design parameter can enhance detectability properties. In this way, it is possible to pose the FDI problem as the solution to a set of linear matrix inequalities which do not restrict the value of the performance variable as strictly as in some other approaches. In addition, it is possible to intuitively offset detectability/isolation properties and robustness to signal uncertainty. The paper demonstrates the effectiveness of the proposed synthesis technique through a simulation example.