An LMI-based robust fault detection and isolation in linear stochastic systems

Here, a new fault detection and isolation (FDI) method based on linear optimisation is proposed for stochastic linear systems with unknown inputs. The stochastic system is discrete and its state and output equations are dependent on unknown inputs. Both stochastic/deterministic unknown inputs (external disturbances) and measurement noise are considered in the dynamic model; therefore, a simple and complete formulation of the robust FDI scheme is presented for stochastic systems. According to the proposed method, first an observable and controllable subsystem is found such that it is independent of the effect of unknown inputs. Then an innovation filter is used for the FDI task. Sufficient conditions to guarantee the stability and observability of the new subsystem are presented based on linear matrix inequalities. Simulation results demonstrate the effectiveness and capability of the proposed method for FDI in stochastic systems with unknown inputs.