Criterions for Detectability and Strong Detectability of Faults in Linear Systems

A fault is (strongly) detectable if it is possible to construct a residual generator that is sensitive to the (constant) fault while decoupling all disturbances. Two new fault detectability criterions and three new strong fault detectability criterions are presented. For comparison, existing fault detectability criterions are reviewed. To prove the criterions, a framework of polynomial bases is utilized. With the set of new criterions, together with the previously known, there exists now a criterion for models given both on transfer function form and state-space form, and for both fault detectability and strong fault detectability investigations. Recommendations are given on what criterion to use in different situations.