  This paper studies the exponential stabilization of a Boussinesq system
describing the two-way propagation of small amplitude gravity waves on the
surface of an ideal fluid, the so-called Boussinesq system of the Korteweg-de
Vries type. We use a Gramian-based method introduced by Urquiza to design our
feedback control. By means of spectral analysis and Fourier expansion, we show
that the solutions of the linearized system decay uniformly to zero when the
feedback control is applied. The decay rate can be chosen as large as we want.
The main novelty of our work is that we can exponentially stabilize this system
of two coupled equations using only one scalar input.
