Efficient computation of Lyapunov functions for nonlinear systems by integrating numerical solutions

Sigurdur Freyr Hafstein*, Asgeir Valfells

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

A strict Lyapunov function for an equilibrium of a dynamical system asserts its asymptotic stability and gives a lower bound on its basin of attraction. For nonlinear systems, the explicit construction of a Lyapunov function taking the nonlinear dynamics into account remains a difficult problem and one often resorts to numerical methods. We improve and analyse a method that is based on a converse theorem in the Lyapunov stability theory and compare it to different methods in the literature. Our method is of low complexity, and its workload is perfectly parallel. Further, its free parameters allow it to be adapted to the problem at hand and we show that our method matches or gives a larger lower bound on the equilibrium’s basin of attraction than other approaches in the literature in most examples. Finally, we apply our method to a model of a genetic toggle switch in Escherichia coli and we demonstrate that our novel method delivers important information on the model’s dynamics for different parameters.

Original languageEnglish
Pages (from-to)1895-1910
Number of pages16
JournalNonlinear Dynamics
Volume97
Issue number3
DOIs
Publication statusPublished - 1 Aug 2019

Bibliographical note

Publisher Copyright:
© 2018, Springer Nature B.V.

Other keywords

  • Basin of attraction
  • Lyapunov function
  • Nonlinear system
  • Numerical method

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