  We are interested in the feedback stabilization of general linear
multi-dimensional first order hyperbolic systems in $\R^d$. 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.
