  We consider the stabilizability of a fluid-structure interaction system where
the fluid is viscous and compressible and the structure is a rigid ball. The
feedback control of the system acts on the ball and corresponds to a force that
would be produced by a spring and a damper connecting the center of the ball to
a fixed point $h_1$. We prove the global-in-time existence of strong solutions
for the corresponding system under a smallness condition on the initial
velocities and on the distance between the initial position of the center of
the ball and $h_1$. Then, we show with our feedback law, that the fluid and the
structure velocities go to 0 and that the center of the ball goes to $h_1$ as
$t\to \infty$.
