Spectral structures of the generalized companion form and applications

In this note, we investigate the relationship between the finite and infinite frequency structure of a regular polynomial matrix and that of a particular linearization, called the generalised companion matrix. A special resolvent decomposition of the regular polynomial matrix is proposed which is based on the Weierstrass canonical form of this generalised companion matrix and the solution of a regular PMD is thus formulated from this resolvent decomposition. Both the initial conditions of the pseudo state and the input are considered.