<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Limits of stabilization of a networked hyperbolic system with a circle

Department Mathematik, Chair in Dynamics, Control, Numerics and Machine Learning (Alexander von Humboldt-Professorship)

Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Limits of stabilization of a networked hyperbolic system with a circle"}

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...

Limits of stabilization of a networked hyperbolic system with a circle

Published Online: Feb 24, 2024

Page range: 79 - 121

Received: Jan 01, 2023

Accepted: Aug 01, 2023

DOI: https://doi.org/10.2478/candc-2023-0033

Keywords
hyperbolic system, exponential stability, circle, network

© 2023 Martin Gugat et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Limits of stabilization of a networked hyperbolic system with a circle

Published Online: Feb 24, 2024

Page range: 79 - 121

Received: Jan 01, 2023

Accepted: Aug 01, 2023

DOI: https://doi.org/10.2478/candc-2023-0033

Keywordshyperbolic system, exponential stability, circle, network

© 2023 Martin Gugat et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
hyperbolic system, exponential stability, circle, network