Extraction of infinite zeros of polynomial matrices

An algorithm is described for computing the structure at infinity and extracting the infinite zeros of a given polynomial matrix. The algorithm relies on numerically reliable operations only. Applications include computation of the subspace of the impulsive solution of a set of linear differential equations, derivation of the Smith form at infinity of a polynomial matrix, and also enhanced computation of the poles of a linear system described by polynomial matrix fractions. The numerical routines described in the paper are implemented in release 3.0 of the Polynomial Toolbox for MATLAB.