Input-to-state stability of a scalar conservation law with nonlocal velocity

Göttlich, Simone ; Herty, Michael ; Weldegiyorgis, Gediyon

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URN: urn:nbn:de:bsz:180-madoc-600240
Document Type: Article
Year of publication: 2021
The title of a journal, publication series: Axioms
Volume: 10
Issue number: 1, Article 12
Page range: 1-20
Place of publication: Basel
Publishing house: MDPI
ISSN: 2075-1680
Related URLs:
Publication language: English
Institution: School of Business Informatics and Mathematics > Wissenschaftliches Rechnen (Göttlich 2011-)
Pre-existing license: Creative Commons Attribution 4.0 International (CC BY 4.0)
Subject: 510 Mathematics
Keywords (English): conservation laws , feedback stabilization , input-to-state stability , numerical approximations , nonlocal velocity
Abstract: In this paper, we study input-to-state stability (ISS) of an equilibrium for a scalar conservation law with nonlocal velocity and measurement error arising in a highly re-entrant manufacturing system. By using a suitable Lyapunov function, we prove sufficient and necessary conditions on ISS. We propose a numerical discretization of the scalar conservation law with nonlocal velocity and measurement error. A suitable discrete Lyapunov function is analyzed to provide ISS of a discrete equilibrium for the proposed numerical approximation. Finally, we show computational results to validate the theoretical findings.
Additional information: Online-Ressource

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