Limits of stabilization of a networked hyperbolic system with a circle
Gugat M, Huang X, Wang Z (2023)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2023
Journal
Book Volume: 52
Pages Range: 79-121
Journal Issue: 1
URI: http://control.ibspan.waw.pl:3000/contents/list?year=2023
Open Access Link: http://control.ibspan.waw.pl:3000/contents/show/214?year=2023
Abstract
This paper is devoted to the discussion of the exponential stability of a networked hyperbolic system with a circle. Our analysis extends an example by Bastin and Coron about the limits of boundary stabilizability of hyperbolic systems to the case of a networked system that is defined on a graph which contains a cycle.
By spectral analysis, we prove that the system is stabilizable while the length of the arcs is sufficiently small. However, if the length of the arcs is too large, the system is not stabilizable. Our results are robust with respect to small perturbations of the arc lengths.
Complementing our analysis, we provide numerical simulations that illustrate our findings.
Authors with CRIS profile
Martin Gugat
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Xu Huang
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
China (CN)How to cite
APA:
Gugat, M., Huang, X., & Wang, Z. (2023). Limits of stabilization of a networked hyperbolic system with a circle. Control and Cybernetics, 52(1), 79-121. https://dx.doi.org/10.2478/candc-2023-0033
MLA:
Gugat, Martin, Xu Huang, and Zhiqiang Wang. "Limits of stabilization of a networked hyperbolic system with a circle." Control and Cybernetics 52.1 (2023): 79-121.
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