Stability and response bounds of non-conservative linear systems

Christian Pommer

Stability and response bounds of non-conservative linear systems

Christian Pommer

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Abstract

For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov function is used to derive amplitude bounds of displacement and velocity in the homogeneous as well as in the inhomogeneous case. The developed results are illustrated by examples.

Original language	English
Title of host publication	2003 International Conference Physics and Control. Proceedings.
Volume	4
Publisher	IEEE
Publication date	2003
Pages	1106-1109
ISBN (Print)	0-7803-7939-X
Publication status	Published - 2003
Event	International Conference on Physics and Control (PHYSCON 2003) - St. Petersburg, Russian Federation Duration: 20 Aug 2003 → 22 Aug 2003

Conference

Conference	International Conference on Physics and Control (PHYSCON 2003)
Country/Territory	Russian Federation
City	St. Petersburg
Period	20/08/2003 → 22/08/2003

Bibliographical note

Copyright: 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

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title = "Stability and response bounds of non-conservative linear systems",

abstract = "For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov function is used to derive amplitude bounds of displacement and velocity in the homogeneous as well as in the inhomogeneous case. The developed results are illustrated by examples. ",

author = "Christian Pommer",

note = "Copyright: 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE; International Conference on Physics and Control (PHYSCON 2003), PHYSCON 2003 ; Conference date: 20-08-2003 Through 22-08-2003",

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N1 - Copyright: 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

PY - 2003

Y1 - 2003

N2 - For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov function is used to derive amplitude bounds of displacement and velocity in the homogeneous as well as in the inhomogeneous case. The developed results are illustrated by examples.

AB - For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov function is used to derive amplitude bounds of displacement and velocity in the homogeneous as well as in the inhomogeneous case. The developed results are illustrated by examples.

M3 - Article in proceedings

SN - 0-7803-7939-X

VL - 4

SP - 1106

EP - 1109

BT - 2003 International Conference Physics and Control. Proceedings.

PB - IEEE

T2 - International Conference on Physics and Control (PHYSCON 2003)

Y2 - 20 August 2003 through 22 August 2003

ER -

Stability and response bounds of non-conservative linear systems

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Conference

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