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

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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 languageEnglish (US)
Pages (from-to)50-53
Number of pages4
JournalSystems and Control Letters
Volume121
DOIs
StatePublished - Nov 2018

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Lyapunov functions
Polynomials

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science(all)

Keywords

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

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}",
year = "2018",
month = "11",
doi = "https://doi.org/10.1016/j.sysconle.2018.07.013",
language = "English (US)",
volume = "121",
pages = "50--53",
journal = "Systems and Control Letters",
issn = "0167-6911",
publisher = "Elsevier",

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AU - Ahmadi, Amir Ali

PY - 2018/11

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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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EP - 53

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

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