Forward completeness implies bounded reachable sets for time-delay systems on the state space of essentially bounded measurable functions
arxiv(2024)
摘要
We consider time-delay systems with a finite number of delays in the state
space L^∞×^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^∞×^n.
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