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arXiv · 2403.00387

For time-invariant delay systems, global asymptotic stability does not imply uniform global attractivity

Antoine Chaillet·Fabian Wirth·Andrii Mironchenko·Lucas Brivadis
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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.

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Antoine Chaillet, Fabian Wirth, Andrii Mironchenko, Lucas Brivadis. 2024-03-01. For time-invariant delay systems, global asymptotic stability does not imply uniform global attractivity. https://arxiv.org/abs/2403.00387

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