For time-invariant delay systems, global asymptotic stability does not imply uniform global attractivity
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909124952850432 |
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| author | Chaillet, Antoine Wirth, Fabian Mironchenko, Andrii Brivadis, Lucas |
| author_facet | Chaillet, Antoine Wirth, Fabian Mironchenko, Andrii Brivadis, Lucas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00387 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | For time-invariant delay systems, global asymptotic stability does not imply uniform global attractivity Chaillet, Antoine Wirth, Fabian Mironchenko, Andrii Brivadis, Lucas Systems and Control 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. |
| title | For time-invariant delay systems, global asymptotic stability does not imply uniform global attractivity |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2403.00387 |