# Contraction Metrics by Numerical Integration and Quadrature: Uniform Error Estimate

### Peter Giesl, Sigurdur Hafstein, Iman Mehrabinezhad

#### 2023

#### Abstract

We show that contraction metrics for continuous time dynamical systems can be computed numerically using numerical integration of certain initial value problems with a subsequent numerical quadrature. Further, we show that for any compact subset of an equilibrium’s basin of attraction and any ε > 0, the parameters for the numerical methods, i.e. the integration interval and the step-size, can be chosen such that the error in the contraction metric is less than ε at any point in the compact subset. These results will be used as a part of a numerical method to rigorously compute contraction metrics.

Download#### Paper Citation

#### in Harvard Style

Giesl P., Hafstein S. and Mehrabinezhad I. (2023). **Contraction Metrics by Numerical Integration and Quadrature: Uniform Error Estimate**. In *Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO*; ISBN 978-989-758-670-5, SciTePress, pages 196-205. DOI: 10.5220/0012183300003543

#### in Bibtex Style

@conference{icinco23,

author={Peter Giesl and Sigurdur Hafstein and Iman Mehrabinezhad},

title={Contraction Metrics by Numerical Integration and Quadrature: Uniform Error Estimate},

booktitle={Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO},

year={2023},

pages={196-205},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0012183300003543},

isbn={978-989-758-670-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO

TI - Contraction Metrics by Numerical Integration and Quadrature: Uniform Error Estimate

SN - 978-989-758-670-5

AU - Giesl P.

AU - Hafstein S.

AU - Mehrabinezhad I.

PY - 2023

SP - 196

EP - 205

DO - 10.5220/0012183300003543

PB - SciTePress