Properties of the generalised companion form and application to the solution of regular PMDs

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 the regular polynomial matrix descriptions (PMDs) is thus formulated from this resolvent decomposition. Both the initial conditions of the pseudo state and the input are considered.