Gottlich, SimoneHerty, MichaelWeldegiyorgis, Gediyon Y.2021-08-312021-08-312021-03Göttlich, S.; Herty, M.; Weldegiyorgis, G. Input-to-State Stability of a Scalar Conservation Law with Nonlocal Velocity. Axioms 2021, 10, 12. https://doi.org/10.3390/axioms10010012.2075-1680 (online)10.3390/ axioms10010012http://hdl.handle.net/2263/81565In 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.en© 2020 by the authors. Licensee: MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).Conservation lawsFeedback stabilizationNumerical approximationsNonlocal velocityInput-to-state stability (ISS)Article