  We consider linear control systems of the form $\dot{y}(t)=Ay(t)-\mu B C
y(t)$ where $\mu$ is a positive real parameter, $A$ is the state operator and
generates a linear $C_0-$semigroup of contractions $S(t) $ on a Banach space
$X$, $B$ and $C$ are respectively the operators of control and observability,
which are defined in appropriate spaces in which they are unbounded in some
sense. We aim to show the exponential stability of the above system under
sufficient conditions which are expressed in term of admissibility and
observability properties. The uniform exponential stabilization using bilinear
control is considered as well. Applications to transport and heat equations are
also provided.
