Robust fault detection for discrete‐time stochastic systems with non‐homogeneous jump processes

The problem of robust fault detection (RFD) is studied for a class of discrete‐time stochastic systems with non‐homogeneous jump processes. First, a filter‐based residual signal generator is constructed. To guarantee the sensitivity to faults and robustness against unknown inputs, both H ∞ performance and a new performance index are considered. Then an FD filter, which minimises the influences of the disturbances, modelling uncertainties and increases the sensitivity to faults, is designed. A sufficient condition for ensuring the existence of RFD filter in terms of linear‐matrix inequalities is established. A simulation is carried out, illustrating that the proposed RFD filter can detect the faults after their occurrences in a timely manner.