Input-to-state stability of a scalar conservation law with nonlocal velocity

TL;DR

This paper investigates the input-to-state stability of a scalar conservation law with nonlocal velocity, providing theoretical conditions, numerical analysis, and simulations to validate stability in manufacturing systems.

Contribution

It introduces a Lyapunov-based approach to establish necessary and sufficient conditions for ISS in both continuous and discrete scalar conservation laws with nonlocal velocity.

Findings

Derived ISS conditions using Lyapunov functions

Validated theoretical results through numerical simulations

Analyzed discretization effects on ISS stability

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.