On a homeomorphism between orbit spaces of linear systems and matrix polynomials

The orbit space of controllable systems under system similarity and the orbit space of matrix polynomials with determinant degree equal to the order of the state matrix under right equivalence are proved to be homeomorphic when the quotient compact–open topology is considered in the latter. As a consequence, the variation of the finite and left Wiener–Hopf structures under small perturbations of matrix polynomials with fixed degree for their determinants is described.