Fault detection and isolation for linear time-invariant systems

This paper is concerned with the problem of detecting and isolating faults by an observer. If the initial error of state estimation is zero, the authors show that faults can be isolated if and only if the system has a left-invertible detectability matrix which is defined in the present paper. For the more realistic case of nonzero initial error of state estimation, the authors develop fault isolation filters such that failures to be detected can be asymptotically isolated. The authors give necessary and sufficient conditions for the existence of such filters. The authors provide a method to design a fault isolation filter. This design procedure guarantees to isolate up to n faults, where n is the dimension of the system