Positively Invariant Sets for ODEs and Numerical Integration

Peter Giesl, Sigurdur Hafstein, Iman Mehrabinezhad

2023

Abstract

We show that for an ordinary differential equation (ODE) with an exponentially stable equilibrium and any compact subset of its basin of attraction, we can find a larger compact set that is positively invariant for both the dynamics of the system and a numerical method to approximate its solution trajectories. We establish this for both one-step numerical integrators and multi-step integrators using sufficiently small time-steps. Further, we show how to localize such sets using continuously differentiable Lyapunov-like functions and numerically computed continuous, piecewise affine (CPA) Lyapunov-like functions.

Paper Citation

in Harvard Style

Giesl P., Hafstein S. and Mehrabinezhad I. (2023). Positively Invariant Sets for ODEs and Numerical Integration. 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 44-53. DOI: 10.5220/0012189700003543

in Bibtex Style

@conference{icinco23,
author={Peter Giesl and Sigurdur Hafstein and Iman Mehrabinezhad},
title={Positively Invariant Sets for ODEs and Numerical Integration},
booktitle={Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO},
year={2023},
pages={44-53},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012189700003543},
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 - Positively Invariant Sets for ODEs and Numerical Integration
SN - 978-989-758-670-5
AU - Giesl P.
AU - Hafstein S.
AU - Mehrabinezhad I.
PY - 2023
SP - 44
EP - 53
DO - 10.5220/0012189700003543
PB - SciTePress