  In this paper we investigate the uniform exponential stability of the system
$\frac{dx(t)}{dt}=Ax(t)-\rho Bx(t), \; (\rho >0), $ where the unbounded
operator $A$ is the infinitesimal generator of a linear $C_0-$semigroup of
contractions $S(t)$ in a Hilbert space $X$ and $B$ is a Desch-Schappacher
operator. Then we give sufficient conditions for exponential stability of the
above system. The obtained stability result is then applied to show the uniform
exponential stabilization of bilinear partial differential equations.
