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In this paper, we provide novel characterizations of the weakly unobservableand the strongly reachable subspaces corresponding to a given state-spacesystem. These characterizations provide closed-form representations for thesaid subspaces. In this process, we establish that the strongly reachablesubspace is intimately related to the space of admissible impulsive inputs. Wealso show how to calculate the dimensions of these subspaces from the transfermatrix of the system.

A matrix theoretic characterization of the strongly reachable subspace