  For abstract linear systems in Hilbert spaces we revisit the problems of
exact controllability and complete stabilizability (stabilizability with an
arbitrary decay rate), the latter property is equivalent to exact null
controllability. We extend this result to the case when the feedback is not
bounded. This enables the characterization of exact null controllability and
complete stabilizability for neutral type systems. By duality, we obtain a
result about continuous final observability.Illustrative examples are given.
