An error bound for model reduction of Lur'e-type systems

B. Besselink; N. Wouw, van de; H. Nijmeijer

doi:10.1109/CDC.2009.5400886

An error bound for model reduction of Lur'e-type systems

B. Besselink
, N. Wouw, van de
, H. Nijmeijer

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

13 Citations (Scopus)

269 Downloads (Pure)

Abstract

In general, existing model reduction techniques for stable nonlinear systems lack a guarantee on stability of the reduced-order model, as well as an error bound. In this paper, a model reduction procedure for absolutely stable Lur’e-type systems is presented, where conditions to ensure absolute stability of the reduced-order model as well as an error bound are given. The proposed model reduction procedure exploits linear model reduction techniques for the reduction of the linear part of the Lur’e-type system. Hence, the proposed model reduction strategy is computationally attractive. Moreover, both stability and the error bound for the obtained reduced-order model hold for an entire class of nonlinearities. The results are illustrated by application to a nonlinear mechanical system.

Original language	English
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	3264-3269
ISBN (Print)	978-1-4244-3871-6
DOIs	https://doi.org/10.1109/CDC.2009.5400886
Publication status	Published - 2009

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Besselink, B., Wouw, van de, N., & Nijmeijer, H. (2009). An error bound for model reduction of Lur'e-type systems. In Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China (pp. 3264-3269). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2009.5400886

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title = "An error bound for model reduction of Lur'e-type systems",

abstract = "In general, existing model reduction techniques for stable nonlinear systems lack a guarantee on stability of the reduced-order model, as well as an error bound. In this paper, a model reduction procedure for absolutely stable Lur{\textquoteright}e-type systems is presented, where conditions to ensure absolute stability of the reduced-order model as well as an error bound are given. The proposed model reduction procedure exploits linear model reduction techniques for the reduction of the linear part of the Lur{\textquoteright}e-type system. Hence, the proposed model reduction strategy is computationally attractive. Moreover, both stability and the error bound for the obtained reduced-order model hold for an entire class of nonlinearities. The results are illustrated by application to a nonlinear mechanical system.",

author = "B. Besselink and \{Wouw, van de\}, N. and H. Nijmeijer",

year = "2009",

doi = "10.1109/CDC.2009.5400886",

language = "English",

isbn = "978-1-4244-3871-6",

pages = "3264--3269",

booktitle = "Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

}

Besselink, B, Wouw, van de, N & Nijmeijer, H 2009, An error bound for model reduction of Lur'e-type systems. in Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China. Institute of Electrical and Electronics Engineers, Piscataway, pp. 3264-3269. https://doi.org/10.1109/CDC.2009.5400886

An error bound for model reduction of Lur'e-type systems. / Besselink, B.; Wouw, van de, N.; Nijmeijer, H.
Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China. Piscataway: Institute of Electrical and Electronics Engineers, 2009. p. 3264-3269.

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

TY - GEN

T1 - An error bound for model reduction of Lur'e-type systems

AU - Besselink, B.

AU - Wouw, van de, N.

AU - Nijmeijer, H.

PY - 2009

Y1 - 2009

N2 - In general, existing model reduction techniques for stable nonlinear systems lack a guarantee on stability of the reduced-order model, as well as an error bound. In this paper, a model reduction procedure for absolutely stable Lur’e-type systems is presented, where conditions to ensure absolute stability of the reduced-order model as well as an error bound are given. The proposed model reduction procedure exploits linear model reduction techniques for the reduction of the linear part of the Lur’e-type system. Hence, the proposed model reduction strategy is computationally attractive. Moreover, both stability and the error bound for the obtained reduced-order model hold for an entire class of nonlinearities. The results are illustrated by application to a nonlinear mechanical system.

AB - In general, existing model reduction techniques for stable nonlinear systems lack a guarantee on stability of the reduced-order model, as well as an error bound. In this paper, a model reduction procedure for absolutely stable Lur’e-type systems is presented, where conditions to ensure absolute stability of the reduced-order model as well as an error bound are given. The proposed model reduction procedure exploits linear model reduction techniques for the reduction of the linear part of the Lur’e-type system. Hence, the proposed model reduction strategy is computationally attractive. Moreover, both stability and the error bound for the obtained reduced-order model hold for an entire class of nonlinearities. The results are illustrated by application to a nonlinear mechanical system.

U2 - 10.1109/CDC.2009.5400886

DO - 10.1109/CDC.2009.5400886

M3 - Conference contribution

SN - 978-1-4244-3871-6

SP - 3264

EP - 3269

BT - Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference (CDC / CCC), 16-18 December 2009, Shanghai, China

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

ER -

An error bound for model reduction of Lur'e-type systems

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