Forward completeness implies bounded reachable sets for time-delay systems on the state space of essentially bounded measurable functions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909134024081408 |
|---|---|
| author | Brivadis, Lucas Chaillet, Antoine Mironchenko, Andrii Wirth, Fabian |
| author_facet | Brivadis, Lucas Chaillet, Antoine Mironchenko, Andrii Wirth, Fabian |
| contents | 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 $L^\infty\times\mathbb{R}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06543 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Forward completeness implies bounded reachable sets for time-delay systems on the state space of essentially bounded measurable functions Brivadis, Lucas Chaillet, Antoine Mironchenko, Andrii Wirth, Fabian Optimization and Control 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 $L^\infty\times\mathbb{R}^n$. |
| title | Forward completeness implies bounded reachable sets for time-delay systems on the state space of essentially bounded measurable functions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2403.06543 |