An example of a GAS system which can be destabilized by an integrable perturbation

Eduardo D. Sontag; Mikhail Krichman

doi:10.1109/TAC.2003.812801

An example of a GAS system which can be destabilized by an integrable perturbation

Eduardo D. Sontag, Mikhail Krichman

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21 Scopus citations

Abstract

A construction of a globally asymptotically stable (GAS) time-invariant system which can be destabilized by an integrable perturbation was presented. Besides its intrinsic interest, this served to provide counterexamples to an open question regarding Lyapunov functions. The original system has convergent spiral trajectories and the coordinate change will be of the accordion type mentioned in the intuitive description.

Original language	English (US)
Pages (from-to)	1046-1049
Number of pages	4
Journal	IEEE Transactions on Automatic Control
Volume	48
Issue number	6
DOIs	https://doi.org/10.1109/TAC.2003.812801
State	Published - Jun 2003

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

Keywords

Asymptotic stability
Integrable perturbations
Intergral stability

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10.1109/TAC.2003.812801

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title = "An example of a GAS system which can be destabilized by an integrable perturbation",

abstract = "A construction of a globally asymptotically stable (GAS) time-invariant system which can be destabilized by an integrable perturbation was presented. Besides its intrinsic interest, this served to provide counterexamples to an open question regarding Lyapunov functions. The original system has convergent spiral trajectories and the coordinate change will be of the accordion type mentioned in the intuitive description.",

keywords = "Asymptotic stability, Integrable perturbations, Intergral stability",

author = "Sontag, {Eduardo D.} and Mikhail Krichman",

note = "Funding Information: Manuscript received December 5, 2002; revised February 11, 2003. Recommended by Associate Editor Z.-P. Jiang. This work was supported in part by the United States Air Force under Grant F49620-01-1-0063. The authors are with the Department of Mathematics, Rutgers University, New Brunswick, NJ 08903 USA. Digital Object Identifier 10.1109/TAC.2003.812801",

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AU - Sontag, Eduardo D.

AU - Krichman, Mikhail

N1 - Funding Information: Manuscript received December 5, 2002; revised February 11, 2003. Recommended by Associate Editor Z.-P. Jiang. This work was supported in part by the United States Air Force under Grant F49620-01-1-0063. The authors are with the Department of Mathematics, Rutgers University, New Brunswick, NJ 08903 USA. Digital Object Identifier 10.1109/TAC.2003.812801

PY - 2003/6

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N2 - A construction of a globally asymptotically stable (GAS) time-invariant system which can be destabilized by an integrable perturbation was presented. Besides its intrinsic interest, this served to provide counterexamples to an open question regarding Lyapunov functions. The original system has convergent spiral trajectories and the coordinate change will be of the accordion type mentioned in the intuitive description.

AB - A construction of a globally asymptotically stable (GAS) time-invariant system which can be destabilized by an integrable perturbation was presented. Besides its intrinsic interest, this served to provide counterexamples to an open question regarding Lyapunov functions. The original system has convergent spiral trajectories and the coordinate change will be of the accordion type mentioned in the intuitive description.

KW - Asymptotic stability

KW - Integrable perturbations

KW - Intergral stability

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An example of a GAS system which can be destabilized by an integrable perturbation

Abstract

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