EHP를 이용한 이산시간에서의 비정형 위너호프 분해

Abstract

We propose a non-canonical spectral 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.

This paper has two aims related to the non-canonical spectral factorization. First, when the state space realization of a para-hermitian rational matrix function is given, how one finds spectral factors in the explicit form using the EHP. Second, we consider the characteristics of the spectral factors derived. The center factor can not be factorized any more according to the proposed algorithm and the inverse of the right spectral factor is stable. Also, the factorization is not a minimal factorization.

The factorization may be applied to parametrizing the optimal or suboptimal solutions of the Nehari problem and the H-infinity problem. We show an example for the application of the proposed algorithm to the optimal or suboptimal Nehari problem.