A closed-form expression for the fault detection filter

This paper presents a novel interpretation of the detection filter in the context of an eigenstructure assignment problem. The detection filter is shown to be equivalent to the combination of two decoupled observers, with the advantage that theories already developed for conventional observers can be utilized as design aids. Detection space and detection order are re-defined accordingly, and it is shown that of the two observers that constitute a detection filter, the one associated with the detection space is a single-output system. This fact is important since it explains important properties of the fault detection filter in a very uncomplicated fashion, leading to a clear interpretation of the freedom available in designing the filter; in particular, it is proven that the detection filter gains are unique, given the eigenvalues of the detection space. Further, the formulation leads to a closed-form expression for the detection filter, and is therefore well-suited to the development of simple design algorithms