Boundary feedback control for hyperbolic systems

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.