Limits of stabilization of a networked hyperbolic system with a circle

• Autorzy: Gugat Martin , Huang Xu , Wang Zhiqiang

Identyfikatory

DOI

10.2478/candc-2023-0033

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hyperbolic system; exponential stability; circle; network

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2023
• Tom: Vol. 52, No. 1
• Strony: 79--121
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Gugat Martin

• Department Mathematik, Chair in Dynamics, Control, Numerics and Machine Learning (Alexander von Humboldt-Professorship), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstr. 11, 91058 Erlangen, Germany

autor

Huang Xu

• School of Mathematical Sciences, Fudan University, Shanghai 200433, China

autor

Wang Zhiqiang

• School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China

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