On the approximation of fault directions for mutual detectability: an invariant zero approach

This note is concerned with the approximation of fault directions in relation to mutual detectability in detection filter problems. As an efficient system representation for analysis of detection order, we utilize the observer canonical form, by which we show that the invariant zero and the detection order can be analytically calculated by a set of polynomials associated with fault directions. Noting that this approach clearly shows the condition for the detection order to be plural, we propose a fault direction approximation method, which increases its detection order, for obtaining a mutually detectable system. Regarding the resulting degradation of fault isolation performance as a disturbance, we present its quantitative analysis and propose a method of selecting a threshold in order to guarantee proper fault isolation.