For time-invariant delay systems, global asymptotic stability does not imply uniform global attractivity
<|reference_start|>For time-invariant delay systems, global asymptotic stability does not imply uniform global attractivity: 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.<|reference_end|>
@article{chaillet2024for,
    title={For time-invariant delay systems, global asymptotic stability does not
  imply uniform global attractivity},
    author={Antoine Chaillet (IUF, L2S), Fabian Wirth, Andrii Mironchenko, Lucas
  Brivadis (L2S)},
    journal={IEEE Conference on Decision and Control, Dec 2024, Milan (Italie),
  Italy},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.00387},
    primaryClass={eess.SY cs.SY}
}