  This work deals with the local rapid exponential stabilization for a
Boussinesq system of KdV-KdV type introduced by J. Bona, M. Chen and J.-C.
Saut. This is a model for the motion of small amplitude long waves on the
surface of an ideal fluid. Here, we will consider the Boussinesq system of
KdV-KdV type posed on a finite domain, with homogeneous Dirichlet--Neumann
boundary controls acting at the right end point of the interval. Our goal is to
build suitable integral transformations to get a feedback control law that
leads to the stabilization of the system. More precisely, we will prove that
the solution of the closed-loop system decays exponentially to zero in the
$L^2(0,L)$--norm and the decay rate can be tuned to be as large as desired if
the initial data is small enough.
