  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.
