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

Title data

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. Vol. 8 (2024) . - pp. 1667-1672.
ISSN 2475-1456
DOI: https://doi.org/10.1109/LCSYS.2024.3408103

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Project information

Project title:
Project's official title
Project's id
Lyapunov theory meets boundary control systems
MI 1886/2-2
Input-to-State Stability of Systems With Delays
FK-20-2022

Project financing: Deutsche Forschungsgemeinschaft
Andere
Franco-Bavarian University Cooperation Center (BayFrance)

Abstract in another language

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 $L^∞ × R^n$.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: nonlinear control systems; time-delay systems; infinite-dimensional systems; forward completeness; input-to-state stability
Subject classification: Mathematics Subject Classification Code: 93B03 (93C43 93D20)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 06 Mar 2025 13:02
Last Modified: 07 Mar 2025 07:06
URI: https://eref.uni-bayreuth.de/id/eprint/92640