Input-to-state stability of a scalar conservation law with nonlocal velocity
Optimization and Control
2020-11-09 v1 Numerical Analysis
Numerical Analysis
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 also analyze the numerical discretization of ISS for a discrete scalar conservation law with nonlocal velocity and measurement error. A suitable discretized Lyapunov function is also analyzed to provide ISS of an equilibrium for the numerical approximation. Finally, we show numerical simulations to validate the theoretical findings.
Keywords
Cite
@article{arxiv.2011.03393,
title = {Input-to-state stability of a scalar conservation law with nonlocal velocity},
author = {Simone Göttlich and Michael Herty and Gediyon Weldegiyorgis},
journal= {arXiv preprint arXiv:2011.03393},
year = {2020}
}
Comments
AMS-LaTeX v1.4.3, 16 pages with 2 figures