Further results on polynomial characterizations of ( )-invariant and reachability subspaces

This paper is concerned with further development of the unification between polynomial matrix and geometric theories of linear systems following the work of Emre and Hautus. Equivalence between different polynomial characterizations of ( )-invariant and reachability subspaces is shown explicitly. Several new results are given which clarify the relations between the polynomial system matrix, invariant subspaces, and system zeros. Finally, a polynomial characterization of and a constructive procedure to obtain the largest stabilizability subspace in ker are given.