Failure identification for linear repetitive processes

This paper investigates the fault detection and isolation (FDI) problem for discrete-time linear repetitive processes using a geometric approach, starting from a 2-D model for these processes that incorporates a representation of the failure. Based on this model, the FDI problem is formulated in the geometric setting and sufficient conditions for solvability of this problem are given. Moreover, the processes's behaviour in the presence of noise is considered, leading to the development of a statistical approach for determining a decision threshold. Finally, a FDI procedure is developed based on an asymptotic observer reconstruction of the state vector.