  The paper provides results for the application of boundary feedback control
with Zero-Order-Hold (ZOH) to 1-D linear parabolic systems on bounded domains.
It is shown that the continuous-time boundary feedback applied in a
sample-and-hold fashion guarantees closed-loop exponential stability, provided
that the sampling period is sufficiently small. Two different continuous-time
feedback designs are considered: the reduced model design and the backstepping
design. The obtained results provide stability estimates for weighted 2-norms
of the state and robustness with respect to perturbations of the sampling
schedule is guaranteed.
