Skew-prime polynomial matrices: The polynomial-model approach

We examine the concept of skew-primeness of polynomial matrices in terms of the associated polynomial model. It is shown that skew-primeness can be characterized in terms of the property of decomposition of a vector space relative to an endomorphism. This basic result is then applied to the special case of nonsingular polynomial matrices. We investigate the nonuniqueness of skew-complements of a skew-prime pair. It is shown that the space of equivalence classes of skew-complements is in bijective correspondence with a finite-dimensional linear space. Finally, the equivalence of the solutions to the problem of output regulation with internal stability obtained via geometric methods and via polynomial matrix techniques is shown explicitly.