Non-minimal Spectral Factorization of a Descriptor System

Abstract

Given a descriptor (singular) system whose transfer function matrix is analytic and invertible on a Cauchy contour, we use state-space realizations to construct the spectral factorization of the transfer function matrix with respect to the Couchy contour in the general case when there is no minimal factorization. Besides the simple algebraic nature of the arguments, we extend the theory of non-minimal Wiener-Hopf factorization of biproper rational matrices to the case of matrices which are polynomial, strictly proper or improper.