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arXiv · 2403.06543

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

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

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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Lucas Brivadis, Antoine Chaillet, Andrii Mironchenko, Fabian Wirth. 2024-03-11. Forward completeness implies bounded reachable sets for time-delay systems on the state space of essentially bounded measurable functions. https://arxiv.org/abs/2403.06543

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