Non-canonical Wiener-Hopf factorization using the extended Hamiltonian pencil in the discrete time

Abstract

This thesis presents an explicit algorithm for a non-canonical Wiener-Hopf factorization of a para-hermitian rational matrix function, based on the extended Hamiltonian pencil method in the discrete time, which does not admit the conventional spectral factorization. The factorization may be applied to parametrizing the optimal or suboptimal solutions of the Nehari problem and the $H^∞$ problem. We also show the properties for the factors derived from the proposed algorithm.