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.
