The University of Southampton
University of Southampton Institutional Repository

An algorithm for the spectral factorization of unimodular para-hermitian polynomial matrices in continuous time

An algorithm for the spectral factorization of unimodular para-hermitian polynomial matrices in continuous time
An algorithm for the spectral factorization of unimodular para-hermitian polynomial matrices in continuous time
In this paper, we address an algorithm for the spectral factorization of para-Hermitian unimodular polynomial matrices in the continuous time case. Most of the algorithms for the spectral factorizations of matrix polynomials depend on the existence of the roots of given polynomial matrices, so it is almost impossible to execute the spectral factorization of unimodular polynomial matrices. In this paper, we provide a new algorithm for the spectral factorization of unimodular polynomial matrices without the existence of the roots of polynomial matrices or the stability. The task one has to do is only to solve a linear matrix inequality consisting of the coefficients of a given unimodular matrix, which can be achieved easily by the use of numerical computation packages. The algorithm
we present here is based on the property of the storage functions for the dissipative systems in which there always exists positive dissipated energy for the environment. This implies that the fundamental property in our algorithm is also a self-standing interesting result with respect to theoretical points of view. Finally, in order to show the validity of our results, we give an illustrative example with respect to numerical aspects.
393-399
Kaneko, Osamu
b06e84b6-acad-41ca-9113-91a2be60696c
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Takaba, Kiyotsugu
951ed1dd-9ead-4dad-bb6f-093c68f52052
Kaneko, Osamu
b06e84b6-acad-41ca-9113-91a2be60696c
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Takaba, Kiyotsugu
951ed1dd-9ead-4dad-bb6f-093c68f52052

Kaneko, Osamu, Rapisarda, Paolo and Takaba, Kiyotsugu (2005) An algorithm for the spectral factorization of unimodular para-hermitian polynomial matrices in continuous time. Transactions of ISCIE, 18 (11), 393-399.

Record type: Article

Abstract

In this paper, we address an algorithm for the spectral factorization of para-Hermitian unimodular polynomial matrices in the continuous time case. Most of the algorithms for the spectral factorizations of matrix polynomials depend on the existence of the roots of given polynomial matrices, so it is almost impossible to execute the spectral factorization of unimodular polynomial matrices. In this paper, we provide a new algorithm for the spectral factorization of unimodular polynomial matrices without the existence of the roots of polynomial matrices or the stability. The task one has to do is only to solve a linear matrix inequality consisting of the coefficients of a given unimodular matrix, which can be achieved easily by the use of numerical computation packages. The algorithm
we present here is based on the property of the storage functions for the dissipative systems in which there always exists positive dissipated energy for the environment. This implies that the fundamental property in our algorithm is also a self-standing interesting result with respect to theoretical points of view. Finally, in order to show the validity of our results, we give an illustrative example with respect to numerical aspects.

PDF
18_393-2.pdf - Other
Download (1MB)

More information

Published date: 2005
Organisations: Vision, Learning and Control

Identifiers

Local EPrints ID: 375498
URI: https://eprints.soton.ac.uk/id/eprint/375498
PURE UUID: bcb5d5ab-bbc9-4cdf-ba3f-d607a6212eeb

Catalogue record

Date deposited: 27 Mar 2015 14:28
Last modified: 17 Jul 2017 21:16

Export record

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×