A matrix theoretic characterization of the strongly reachable subspace

Abstract

In this paper, we provide novel characterizations of the weakly unobservable and the strongly reachable subspaces corresponding to a given state-space system. These characterizations provide closed-form representations for the said subspaces. In this process, we establish that the strongly reachable subspace is intimately related to the space of admissible impulsive inputs. We also show how to calculate the dimensions of these subspaces from the transfer matrix of the system.