No. 2023.15
Boundary feedback control for hyperbolic systems
M. Herty and F. Thein
Subject: Optimization and control, analysis of PDEs
Abstract
We are interested in the feedback stabilization of general linear multi-dimensional first order hyperbolic systems in $\mathbb{R}^d$. Using a Lyapunov function with a suited weight function dpending on the system under consideration we show stabilization in $L^2$ for the studied system using a suitable feedback control. Therefore the controlability of the studied system is related to the feasibility of an associated linear matrix inequality. We show the applicability discussing the barotropic Euler equations.