Output feedback stabilization for a scalar conservation law with a nonlocal velocity

TL;DR

This paper investigates output feedback stabilization of a scalar conservation law with nonlocal velocity, modeling semiconductor manufacturing, providing spectral analysis for linear systems and Lyapunov methods for nonlinear stabilization.

Contribution

It offers a comprehensive spectral analysis for linearized systems and introduces Lyapunov-based stabilization techniques for nonlinear systems with nonlocal velocities.

Findings

Spectral analysis yields complete exponential stabilization results for linearized systems.

Lyapunov functions prove exponential stabilization for nonlinear systems in specific cases.

The methods are applicable to models of highly re-entrant manufacturing processes.

Abstract

In this paper, we study the output feedback stabilization for a scalar conservation law with a nonlocal velocity, that models a highly re-entrant manufacturing system as encountered in semi-conductor production. By spectral analysis, we obtain a complete result on the exponential stabilization for the linearized control system. Moreover, by using a Lyapunov function approach, we also prove the exponential stabilization results for the nonlinear control system in certain cases.