Stability of linear systems in second-order form based on structure preserving similarity transformations

Jakob Stoustrup, Christian Pommer, Wolfhard Kliem

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

This paper deals with two stability aspects of linear systems of the form Ix¨+Bx˙+Cx=0 given by the triple (I, B, C). A general transformation scheme is given for a structure and Jordan form preserving transformation of the triple. We investigate how a system can be transformed by suitable choices of the transformation parameters into a new system (I, B 1, C 1) with a symmetrizable matrix C 1. This procedure facilitates stability investigations. We also consider systems with a Hamiltonian spectrum which discloses marginal stability after a Jordan form preserving transformation.
Original languageEnglish
JournalZeitschrift fuer Angewandte Mathematik und Physik
Volume66
Issue number5
Pages (from-to)2909-2919
ISSN0044-2275
DOIs
Publication statusPublished - 2015

Cite this

@article{e5e743ba197043018c3abb3e719c695c,
title = "Stability of linear systems in second-order form based on structure preserving similarity transformations",
abstract = "This paper deals with two stability aspects of linear systems of the form Ix¨+Bx˙+Cx=0 given by the triple (I, B, C). A general transformation scheme is given for a structure and Jordan form preserving transformation of the triple. We investigate how a system can be transformed by suitable choices of the transformation parameters into a new system (I, B 1, C 1) with a symmetrizable matrix C 1. This procedure facilitates stability investigations. We also consider systems with a Hamiltonian spectrum which discloses marginal stability after a Jordan form preserving transformation.",
author = "Jakob Stoustrup and Christian Pommer and Wolfhard Kliem",
year = "2015",
doi = "10.1007/s00033-015-0548-4",
language = "English",
volume = "66",
pages = "2909--2919",
journal = "Zeitschrift fuer Angewandte Mathematik und Physik",
issn = "0044-2275",
publisher = "Springer Basel AG",
number = "5",

}

Stability of linear systems in second-order form based on structure preserving similarity transformations. / Stoustrup, Jakob; Pommer, Christian; Kliem, Wolfhard.

In: Zeitschrift fuer Angewandte Mathematik und Physik, Vol. 66, No. 5, 2015, p. 2909-2919.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Stability of linear systems in second-order form based on structure preserving similarity transformations

AU - Stoustrup, Jakob

AU - Pommer, Christian

AU - Kliem, Wolfhard

PY - 2015

Y1 - 2015

N2 - This paper deals with two stability aspects of linear systems of the form Ix¨+Bx˙+Cx=0 given by the triple (I, B, C). A general transformation scheme is given for a structure and Jordan form preserving transformation of the triple. We investigate how a system can be transformed by suitable choices of the transformation parameters into a new system (I, B 1, C 1) with a symmetrizable matrix C 1. This procedure facilitates stability investigations. We also consider systems with a Hamiltonian spectrum which discloses marginal stability after a Jordan form preserving transformation.

AB - This paper deals with two stability aspects of linear systems of the form Ix¨+Bx˙+Cx=0 given by the triple (I, B, C). A general transformation scheme is given for a structure and Jordan form preserving transformation of the triple. We investigate how a system can be transformed by suitable choices of the transformation parameters into a new system (I, B 1, C 1) with a symmetrizable matrix C 1. This procedure facilitates stability investigations. We also consider systems with a Hamiltonian spectrum which discloses marginal stability after a Jordan form preserving transformation.

U2 - 10.1007/s00033-015-0548-4

DO - 10.1007/s00033-015-0548-4

M3 - Journal article

VL - 66

SP - 2909

EP - 2919

JO - Zeitschrift fuer Angewandte Mathematik und Physik

JF - Zeitschrift fuer Angewandte Mathematik und Physik

SN - 0044-2275

IS - 5

ER -