  We consider a one-dimensional controlled reaction-diffusion equation, where
the control acts on the boundary and is subject to a constant delay. Such a
model is a paradigm for more general parabolic systems coupled with a transport
equation. We prove that this is possible to stabilize (in H 1 norm) this
process by means of an explicit predictor-based feedback control that is
designed from a finite-dimensional subsystem. The implementation is very simple
and efficient and is based on standard tools of pole-shifting. Our feedback
acts on the system as a finite-dimensional predictor. We compare our approach
with the backstepping method.
