English

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}
}