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 journalArticle

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

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science(all)
  • 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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