  We prove the well-posedness of a linear closed-loop system with an explicit
(already known) feedback leading to arbitrarily large decay rates. We define a
mild solution of the closed-loop problem using a dual equation and we prove
that the original operator perturbed by the feedback is (up to the use of an
extension) the infinitesimal generator of a strongly continuous group. We also
give a justification to the exponential decay of the solutions. Our method is
direct and avoids the use of optimal control theory.
