  The paper provides results for the application of boundary feedback control
with Zero-Order-Hold (ZOH) to 1-D linear, first-order, hyperbolic systems with
non-local terms on bounded domains. It is shown that the emulation design based
on the recently proposed continuous-time, boundary feedback, designed by means
of backstepping, guarantees closed-loop exponential stability, provided that
the sampling period is sufficiently small. It is also shown that, contrary to
the parabolic case, a smaller sampling period implies a faster convergence rate
with no upper bound for the achieved convergence rate. The obtained results
provide stability estimates for the sup-norm of the state and robustness with
respect to perturbations of the sampling schedule is guaranteed.
