Well-posedness and Accuracy of Harmonic Linearization for Lur'e Systems

R.A. Berg, van den; A.Y. Pogromski; J.E. Rooda

doi:10.1109/CDC.2007.4434447

Well-posedness and Accuracy of Harmonic Linearization for Lur'e Systems

R.A. Berg, van den, A.Y. Pogromski, J.E. Rooda

Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

12 Citations (Scopus)

2 Downloads (Pure)

Abstract

In this paper we deal with the performance analysis of harmonically forced nonlinear systems of Lur’e type. We use harmonic linearization to obtain a linear approximation of the nonlinear system, and provide a frequency domain condition that guarantees a unique positive real solution to the harmonic balance equation for a certain class of nonlinearities. Furthermore, we provide an estimate on the error between the solutions of the nonlinear system and its linear approximation. Finally, we give an example to illustrate the presented theory.

Original language	English
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control
Place of Publication	United States, New Orleans
Pages	3841-3846
DOIs	https://doi.org/10.1109/CDC.2007.4434447
Publication status	Published - 2007

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10.1109/CDC.2007.4434447

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title = "Well-posedness and Accuracy of Harmonic Linearization for Lur'e Systems",

abstract = "In this paper we deal with the performance analysis of harmonically forced nonlinear systems of Lur{\textquoteright}e type. We use harmonic linearization to obtain a linear approximation of the nonlinear system, and provide a frequency domain condition that guarantees a unique positive real solution to the harmonic balance equation for a certain class of nonlinearities. Furthermore, we provide an estimate on the error between the solutions of the nonlinear system and its linear approximation. Finally, we give an example to illustrate the presented theory.",

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year = "2007",

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AU - Berg, van den, R.A.

AU - Pogromski, A.Y.

AU - Rooda, J.E.

PY - 2007

Y1 - 2007

N2 - In this paper we deal with the performance analysis of harmonically forced nonlinear systems of Lur’e type. We use harmonic linearization to obtain a linear approximation of the nonlinear system, and provide a frequency domain condition that guarantees a unique positive real solution to the harmonic balance equation for a certain class of nonlinearities. Furthermore, we provide an estimate on the error between the solutions of the nonlinear system and its linear approximation. Finally, we give an example to illustrate the presented theory.

AB - In this paper we deal with the performance analysis of harmonically forced nonlinear systems of Lur’e type. We use harmonic linearization to obtain a linear approximation of the nonlinear system, and provide a frequency domain condition that guarantees a unique positive real solution to the harmonic balance equation for a certain class of nonlinearities. Furthermore, we provide an estimate on the error between the solutions of the nonlinear system and its linear approximation. Finally, we give an example to illustrate the presented theory.

U2 - 10.1109/CDC.2007.4434447

DO - 10.1109/CDC.2007.4434447

M3 - Conference contribution

SN - 978-1-4244-1497-0

SP - 3841

EP - 3846

BT - Proceedings of the 46th IEEE Conference on Decision and Control

CY - United States, New Orleans

ER -

Well-posedness and Accuracy of Harmonic Linearization for Lur'e Systems

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