Remarks on the relationship between ℒp stability and internal stability of nonlinear systems

Xu Wang; H°avard Fjær Grip; Ali Saberi; Anton A. Stoorvogel; Ingmar Saberi

doi:10.1109/ACC.2011.5991498

Remarks on the relationship between ℒ_p stability and internal stability of nonlinear systems

Xu Wang, H°avard Fjær Grip, Ali Saberi, Anton A. Stoorvogel, Ingmar Saberi

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

Abstract

In this paper, we investigate the relationship between ℒ_p stability and internal stability of nonlinear systems. It is shown that under certain conditions, ℒ_p stability without finite gain implies attractivity of the equilibrium, and that local ℒ_p stability with finite gain implies local asymptotic stability of the origin.

Original language	English
Title of host publication	Proceedings of the American Control Conference, ACC 2011
Place of Publication	Piscataway, NJ, USA
Publisher	IEEE Control Systems Society
Pages	1969-1970
Number of pages	6
ISBN (Print)	978-1-4577-0080-4
DOIs	https://doi.org/10.1109/ACC.2011.5991498
Publication status	Published - Jun 2011
Event	2011 American Control Conference, ACC 2011 - San Francisco, United States Duration: 29 Jun 2011 → 1 Jul 2011

Publication series

Name	Proceedings of the American Control Conference
Publisher	IEEE Control Systems Society
Volume	2011
ISSN (Print)	0743-1619

Conference

Conference	2011 American Control Conference, ACC 2011
Abbreviated title	ACC
Country/Territory	United States
City	San Francisco
Period	29/06/11 → 1/07/11

Access to Document

10.1109/ACC.2011.5991498

Cite this

Wang, X., Grip, H. F., Saberi, A., Stoorvogel, A. A., & Saberi, I. (2011). Remarks on the relationship between ℒ_p stability and internal stability of nonlinear systems. In Proceedings of the American Control Conference, ACC 2011 (pp. 1969-1970). (Proceedings of the American Control Conference; Vol. 2011). IEEE Control Systems Society. https://doi.org/10.1109/ACC.2011.5991498

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title = "Remarks on the relationship between ℒp stability and internal stability of nonlinear systems",

abstract = "In this paper, we investigate the relationship between ℒp stability and internal stability of nonlinear systems. It is shown that under certain conditions, ℒp stability without finite gain implies attractivity of the equilibrium, and that local ℒp stability with finite gain implies local asymptotic stability of the origin.",

author = "Xu Wang and Grip, {H°avard Fj{\ae}r} and Ali Saberi and Stoorvogel, {Anton A.} and Ingmar Saberi",

year = "2011",

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doi = "10.1109/ACC.2011.5991498",

language = "English",

isbn = "978-1-4577-0080-4",

series = "Proceedings of the American Control Conference",

publisher = "IEEE Control Systems Society",

pages = "1969--1970",

booktitle = "Proceedings of the American Control Conference, ACC 2011",

note = "2011 American Control Conference, ACC 2011, ACC ; Conference date: 29-06-2011 Through 01-07-2011",

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Wang, X, Grip, HF, Saberi, A, Stoorvogel, AA & Saberi, I 2011, Remarks on the relationship between ℒ_p stability and internal stability of nonlinear systems. in Proceedings of the American Control Conference, ACC 2011. Proceedings of the American Control Conference, vol. 2011, IEEE Control Systems Society, Piscataway, NJ, USA, pp. 1969-1970, 2011 American Control Conference, ACC 2011, San Francisco, California, United States, 29/06/11. https://doi.org/10.1109/ACC.2011.5991498

Remarks on the relationship between ℒ_p stability and internal stability of nonlinear systems. / Wang, Xu; Grip, H°avard Fjær; Saberi, Ali; Stoorvogel, Anton A.; Saberi, Ingmar.

Proceedings of the American Control Conference, ACC 2011. Piscataway, NJ, USA : IEEE Control Systems Society, 2011. p. 1969-1970 (Proceedings of the American Control Conference; Vol. 2011).

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

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AU - Saberi, Ingmar

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AB - In this paper, we investigate the relationship between ℒp stability and internal stability of nonlinear systems. It is shown that under certain conditions, ℒp stability without finite gain implies attractivity of the equilibrium, and that local ℒp stability with finite gain implies local asymptotic stability of the origin.

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DO - 10.1109/ACC.2011.5991498

M3 - Conference contribution

SN - 978-1-4577-0080-4

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Wang X, Grip HF, Saberi A, Stoorvogel AA, Saberi I. Remarks on the relationship between ℒ_p stability and internal stability of nonlinear systems. In Proceedings of the American Control Conference, ACC 2011. Piscataway, NJ, USA: IEEE Control Systems Society. 2011. p. 1969-1970. (Proceedings of the American Control Conference). https://doi.org/10.1109/ACC.2011.5991498