A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function

Amir Ali Ahmadi; Bachir El Khadir

doi:10.1016/j.sysconle.2018.07.013

A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function

Amir Ali Ahmadi, Bachir El Khadir

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.

Original language	English (US)
Pages (from-to)	50-53
Number of pages	4
Journal	Systems and Control Letters
Volume	121
DOIs	https://doi.org/10.1016/j.sysconle.2018.07.013
State	Published - Nov 2018

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

Keywords

Algorithms for testing asymptotic stability
Nonlinear dynamics
Polynomial Lyapunov functions
Polynomial vector fields
Sum of squares optimization

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10.1016/j.sysconle.2018.07.013

Cite this

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title = "A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function",

abstract = "We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.",

keywords = "Algorithms for testing asymptotic stability, Nonlinear dynamics, Polynomial Lyapunov functions, Polynomial vector fields, Sum of squares optimization",

author = "Ahmadi, {Amir Ali} and {El Khadir}, Bachir",

note = "Publisher Copyright: {\textcopyright} 2018",

year = "2018",

month = nov,

doi = "10.1016/j.sysconle.2018.07.013",

language = "English (US)",

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AU - Ahmadi, Amir Ali

AU - El Khadir, Bachir

PY - 2018/11

Y1 - 2018/11

N2 - We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.

AB - We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.

KW - Algorithms for testing asymptotic stability

KW - Nonlinear dynamics

KW - Polynomial Lyapunov functions

KW - Polynomial vector fields

KW - Sum of squares optimization

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DO - 10.1016/j.sysconle.2018.07.013

M3 - Article

AN - SCOPUS:85055021715

SN - 0167-6911

VL - 121

SP - 50

EP - 53

JO - Systems and Control Letters

JF - Systems and Control Letters

ER -

A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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