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Pré-Publication, Document De Travail Année : 2024

Forward completeness implies bounded reachable sets for time-delay systems on the state space of essentially bounded measurable functions

Résumé

We consider time-delay systems with a finite number of delays in the state space $L^\infty\times\mathbb{R}^n$. In this framework, we show that forward completeness implies the bounded reachability sets property, while this implication was recently shown by J.L. Mancilla-Aguilar and H. Haimovich to fail in the state space of continuous functions. As a consequence, we show that global asymptotic stability is always uniform in the state space $L^\infty\times\mathbb{R}^n$.
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Dates et versions

hal-04493683 , version 1 (07-03-2024)

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  • HAL Id : hal-04493683 , version 1

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Lucas Brivadis, Antoine Chaillet, Andrii Mironchenko, Fabian Wirth. Forward completeness implies bounded reachable sets for time-delay systems on the state space of essentially bounded measurable functions. 2024. ⟨hal-04493683⟩
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