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

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Brivadis, Lucas ; Chaillet, Antoine ; Mironchenko, Andrii ; Wirth, Fabian:
Forward completeness implies bounded reachable sets for time-delay systems on the state space of essentially bounded measurable functions.
In: IEEE Control Systems Letters. Bd. 8 (2024) . - S. 1667-1672.
ISSN 2475-1456
DOI: https://doi.org/10.1109/LCSYS.2024.3408103

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Abstract

We consider time-delay systems with a finite number of delays in the state space $L^∞ × R^n$. In this framework, we show that forward completeness implies the bounded reachability sets property. 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 $L^∞ × R^n$.