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
This is a pre-print. The definitive version: PUGH, A.C. and TAN, L., 2002. Spectral structures of the generalized companion form and applications. Systems and Control Letters, 46(2), pp. 75-84.