Robustness of Numerically Computed Contraction Metrics

Peter Giesl, Sigurdur Hafstein, Iman Mehrabinezhad*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Contraction metrics are an important tool to show the existence of exponentially stable equilibria or periodic orbits, and to determine a subset of their basin of attraction. One of the main advantages is that contraction metrics are robust with respect to perturbations of the system, i.e. a contraction metric for one particular system is also a contraction metric for a perturbed system. In this paper, we discuss numerical methods to compute contraction metrics for dynamical systems, with exponentially stable equilibria or periodic orbits, and perform perturbation analysis. In particular, we prove the robustness of such metrics to perturbations of the system and give concrete bounds. The results imply that a contraction metric, computed for a particular system, remains a contraction metric for the perturbed system. We illustrate our results by computing contraction metrics for systems from the literature, both with exponentially stable equilibria and exponentially stable periodic orbits, and then investigate the validity of the metrics for perturbed systems. Parts of the results are published in Giesl et al. (Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics (ICINCO), 2021).

Original languageEnglish
Article number257
JournalSN Computer Science
Issue number4
Publication statusPublished - 29 Apr 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.

Other keywords

  • Contraction metric
  • Dynamical system
  • Equilibrium point
  • Exponentially stable
  • Periodic orbit
  • Radial basis functions


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