Boundary feedback control for hyperbolic systems

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 depending on the system under consideration we show stabilization in $L^2$ for the studied system using a suitable feedback control. Therefore the controllability of the studied system is related to the feasibility of an associated linear matrix inequality.We show the applicability discussing the barotropic Euler equations.

arXiv admin note: text overlap with arXiv:2207.12006