Operating modes distinguishability condition in switching systems

Abstract

In this paper, we consider a switching system with several operating modes which represent normal or faulty behavior. The objective is to find a necessary and sufficient condition to distinguish these modes through the input/output data. If faulty operation modes are considered the distinguishability condition corresponds to a fault detectability condition. As in [1], we define in this paper two notions of distinguishability: the distinguishability through the input/output data of the system and the distinguishability through the parity residuals of each mode. The Necessary and Sufficient Condition (NSC) of distinguishability through parity-space residuals in [1] was obtained in the case where the parity-space orders are identical in all modes. Here a more generalized NSC of distinguishability is provided for systems which could have different parity-space orders. We show in this context two main results: a NSC of distinguishability through parity residuals which generalizes the NSC in [1] and the equivalence between the two notions of distinguishability. We also demonstrate that the distinguishability definition in [1] is linked to the notion of equivalent representations used in the theory of realization.