560	RWTH Publication No: 811899        2020
TITLE	Input-to-state stability of a scalar conservation law with nonlocal velocity
AUTHORS	Simone Göttlich, Michael Herty, Gediyon Weldegiyorgis
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	Conservation laws, feedback stabilization, input-to-state stability, numerical approximations, nonlocal velocity
DOI	10.3390/axioms10010012
PUBLICATION	Axioms - Differential Models, Numerical Simulations and Applications, 2021