A study on the spectrum of monodromy operator for a time-delay system

Jung Hoon Kim, Tomomichi Hagiwara, Kentaro Hirata

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper studies the spectral properties of mon-odromy operators, which play an important role in stability analysis of linear time-invariant time-delay feedback systems. The paper is motivated by the fact that this operator can actually be defined naturally on four spaces, where the difference stems from different choices for the function space on which the infinite-dimensional state of such a time-delay system is assumed to take its value. It is first shown that the spectrum of the monodromy operator is independent of the spaces on which it is defined. It is further shown that the operator spectrum is continuous at monodromy operators, which is a crucial fundamental fact in justifying the spectrum computation of the monodromy operator through its approximation by any sort of tractable operators.

Original languageEnglish
Title of host publication2013 9th Asian Control Conference, ASCC 2013
DOIs
Publication statusPublished - 2013
Externally publishedYes
Event2013 9th Asian Control Conference, ASCC 2013 - Istanbul, Turkey
Duration: Jun 23 2013Jun 26 2013

Other

Other2013 9th Asian Control Conference, ASCC 2013
CountryTurkey
CityIstanbul
Period6/23/136/26/13

Fingerprint

Time delay
Mathematical operators
Feedback

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Kim, J. H., Hagiwara, T., & Hirata, K. (2013). A study on the spectrum of monodromy operator for a time-delay system. In 2013 9th Asian Control Conference, ASCC 2013 [6606024] https://doi.org/10.1109/ASCC.2013.6606024

A study on the spectrum of monodromy operator for a time-delay system. / Kim, Jung Hoon; Hagiwara, Tomomichi; Hirata, Kentaro.

2013 9th Asian Control Conference, ASCC 2013. 2013. 6606024.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kim, JH, Hagiwara, T & Hirata, K 2013, A study on the spectrum of monodromy operator for a time-delay system. in 2013 9th Asian Control Conference, ASCC 2013., 6606024, 2013 9th Asian Control Conference, ASCC 2013, Istanbul, Turkey, 6/23/13. https://doi.org/10.1109/ASCC.2013.6606024
Kim JH, Hagiwara T, Hirata K. A study on the spectrum of monodromy operator for a time-delay system. In 2013 9th Asian Control Conference, ASCC 2013. 2013. 6606024 https://doi.org/10.1109/ASCC.2013.6606024
Kim, Jung Hoon ; Hagiwara, Tomomichi ; Hirata, Kentaro. / A study on the spectrum of monodromy operator for a time-delay system. 2013 9th Asian Control Conference, ASCC 2013. 2013.
@inproceedings{93dfba0c8e724534946790d16ca89f94,
title = "A study on the spectrum of monodromy operator for a time-delay system",
abstract = "This paper studies the spectral properties of mon-odromy operators, which play an important role in stability analysis of linear time-invariant time-delay feedback systems. The paper is motivated by the fact that this operator can actually be defined naturally on four spaces, where the difference stems from different choices for the function space on which the infinite-dimensional state of such a time-delay system is assumed to take its value. It is first shown that the spectrum of the monodromy operator is independent of the spaces on which it is defined. It is further shown that the operator spectrum is continuous at monodromy operators, which is a crucial fundamental fact in justifying the spectrum computation of the monodromy operator through its approximation by any sort of tractable operators.",
author = "Kim, {Jung Hoon} and Tomomichi Hagiwara and Kentaro Hirata",
year = "2013",
doi = "10.1109/ASCC.2013.6606024",
language = "English",
isbn = "9781467357692",
booktitle = "2013 9th Asian Control Conference, ASCC 2013",

}

TY - GEN

T1 - A study on the spectrum of monodromy operator for a time-delay system

AU - Kim, Jung Hoon

AU - Hagiwara, Tomomichi

AU - Hirata, Kentaro

PY - 2013

Y1 - 2013

N2 - This paper studies the spectral properties of mon-odromy operators, which play an important role in stability analysis of linear time-invariant time-delay feedback systems. The paper is motivated by the fact that this operator can actually be defined naturally on four spaces, where the difference stems from different choices for the function space on which the infinite-dimensional state of such a time-delay system is assumed to take its value. It is first shown that the spectrum of the monodromy operator is independent of the spaces on which it is defined. It is further shown that the operator spectrum is continuous at monodromy operators, which is a crucial fundamental fact in justifying the spectrum computation of the monodromy operator through its approximation by any sort of tractable operators.

AB - This paper studies the spectral properties of mon-odromy operators, which play an important role in stability analysis of linear time-invariant time-delay feedback systems. The paper is motivated by the fact that this operator can actually be defined naturally on four spaces, where the difference stems from different choices for the function space on which the infinite-dimensional state of such a time-delay system is assumed to take its value. It is first shown that the spectrum of the monodromy operator is independent of the spaces on which it is defined. It is further shown that the operator spectrum is continuous at monodromy operators, which is a crucial fundamental fact in justifying the spectrum computation of the monodromy operator through its approximation by any sort of tractable operators.

UR - http://www.scopus.com/inward/record.url?scp=84886513694&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84886513694&partnerID=8YFLogxK

U2 - 10.1109/ASCC.2013.6606024

DO - 10.1109/ASCC.2013.6606024

M3 - Conference contribution

AN - SCOPUS:84886513694

SN - 9781467357692

BT - 2013 9th Asian Control Conference, ASCC 2013

ER -