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

Titelangaben

Chaillet, Antoine ; Wirth, Fabian ; Mironchenko, Andrii ; Brivadis, Lucas:
For time-invariant delay systems, global asymptotic stability does not imply uniform global attractivity.
In: IEEE Control Systems Letters. Bd. 8 (2024) . - S. 484-489.
ISSN 2475-1456
DOI: https://doi.org/10.1109/LCSYS.2024.3396291

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Abstract

Adapting a counter-example 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.