For time-invariant delay systems, global asymptotic stability does not imply uniform global attractivity
Systems and Control
2024-03-04 v1 Systems and Control
Abstract
Adapting a counterexample recently proposed by J.L. Mancilla-Aguilar and H. Haimovich, we show here that, for time-delay systems, global asymptotic stability does not ensure that solutions converge uniformly to zero over bounded sets of initial states. Hence, the convergence might be arbitrarily slow even if initial states are confined to a bounded set.
Keywords
Cite
@article{arxiv.2403.00387,
title = {For time-invariant delay systems, global asymptotic stability does not imply uniform global attractivity},
author = {Antoine Chaillet and Fabian Wirth and Andrii Mironchenko and Lucas Brivadis},
journal= {arXiv preprint arXiv:2403.00387},
year = {2024}
}