  This work is devoted to the stabilization of parabolic systems with a
finite-dimensional control subjected to a constant delay. Our main result shows
that the Fattorini-Hautus criterion yields the existence of such a feedback
control, as in the case of stabilization without delay. The proof consists in
splitting the system into a finite dimensional unstable part and a stable
infinite-dimensional part and to apply the Artstein transformation on the
finite-dimensional system to remove the delay in the control. Using our
abstract result, we can prove new results for the stabilization of parabolic
systems with constant delay: the $N$-dimensional linear convection-diffusion
equation with $N\geq 1$ and the Oseen system. We end the article by showing
that this theory can be used to stabilize nonlinear parabolic systems with
input delay by proving the local feedback distributed stabilization of the
Navier-Stokes system around a stationary state.
