Single-experiment observability decomposition of discrete-time analytic systems

This paper addresses the single-experiment observability decomposition of discrete-time analytic systems. Unlike the continuous-time case, there exist systems which cannot be decomposed into observable and unobservable subsystems due to the fact that the observable space is not integrable. In this paper, a necessary and sufficient condition for integrability of observable space is given. As a corollary of this condition it is proven that if the system is reversible, the observability decomposition can be always achieved. Moreover, integrability of observable space is also addressed for delta-domain models of non-uniformly sampled systems.