10 - Frequency structures of generalized companion form and application to the solution of regular PMDs

Abstract

In this chapter, we investigate the relationship between the finite and infinite frequency structure of a regular polynomial matrix and that of a simply determined companion matrix. It has been shown that in the Weierstrass canonical form of this generalized companion matrix, the finite Jordan block matrices determine the finite zeros of the original polynomial matrix and the sizes of the infinite Jordan block matrices determine the infinite frequency structure of the original polynomial matrix and vice versa. A resolvent decomposition has been proposed based on the Weierstrass canonical form of the companion matrix which is easier to obtain than the finite Jordan pair and the infinite Jordan pair. Subsequently a solution procedure has been developed by using this resolvent decomposition.