A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function

Amir Ali Ahmadi; Miroslav Krstic; Pablo A. Parrilo

doi:10.1109/CDC.2011.6161499

A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function

Amir Ali Ahmadi, Miroslav Krstic, Pablo A. Parrilo

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

54 Scopus citations

Abstract

We give a simple, explicit example of a two-dimensional polynomial vector field that is globally asymptotically stable but does not admit a polynomial Lyapunov function.

Original language	English (US)
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	7579-7580
Number of pages	2
ISBN (Print)	9781612848006
DOIs	https://doi.org/10.1109/CDC.2011.6161499
State	Published - 2011
Externally published	Yes
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: Dec 12 2011 → Dec 15 2011

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/Territory	United States
City	Orlando, FL
Period	12/12/11 → 12/15/11

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2011.6161499

Cite this

Ahmadi, A. A., Krstic, M., & Parrilo, P. A. (2011). A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 7579-7580). Article 6161499 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2011.6161499

Ahmadi, Amir Ali ; Krstic, Miroslav ; Parrilo, Pablo A. / A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function. 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. pp. 7579-7580 (Proceedings of the IEEE Conference on Decision and Control).

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title = "A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function",

abstract = "We give a simple, explicit example of a two-dimensional polynomial vector field that is globally asymptotically stable but does not admit a polynomial Lyapunov function.",

author = "Ahmadi, {Amir Ali} and Miroslav Krstic and Parrilo, {Pablo A.}",

year = "2011",

doi = "10.1109/CDC.2011.6161499",

language = "English (US)",

isbn = "9781612848006",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "7579--7580",

booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",

address = "United States",

note = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",

}

Ahmadi, AA, Krstic, M & Parrilo, PA 2011, A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6161499, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 7579-7580, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6161499

A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function. / Ahmadi, Amir Ali; Krstic, Miroslav; Parrilo, Pablo A.
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. p. 7579-7580 6161499 (Proceedings of the IEEE Conference on Decision and Control).

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

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AU - Krstic, Miroslav

AU - Parrilo, Pablo A.

PY - 2011

Y1 - 2011

N2 - We give a simple, explicit example of a two-dimensional polynomial vector field that is globally asymptotically stable but does not admit a polynomial Lyapunov function.

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DO - 10.1109/CDC.2011.6161499

M3 - Conference contribution

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T3 - Proceedings of the IEEE Conference on Decision and Control

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BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

PB - Institute of Electrical and Electronics Engineers Inc.

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Y2 - 12 December 2011 through 15 December 2011

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Ahmadi AA, Krstic M, Parrilo PA. A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc. 2011. p. 7579-7580. 6161499. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2011.6161499

A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function

Abstract

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All Science Journal Classification (ASJC) codes

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