Conditioned invariance and detectability subspaces in the behavioral approach

Abstract

In this paper we extend the state space geometric notions of conditioned invariance and detectability subspaces to the behavioral framework. This is achieved based on the existing notions of behavioral tracking observer and of behavioral asymptotic observer introduced by Valcher, Willems, Trentelman and Trumph, combined with a notion of behavioral invariance introduced here. Moreover, we provide characterizations for the newly defined behavioral properties.