  It is now well understood that equations of viscoelasticity can be seen as
perturbation of wave type equations. This observation can be exploited in
several different ways and it turns out that it is a usefull tool when studying
controllability. Here we compare a viscoelastic system which fills a surface of
a solid region (the string case has already been studied) with its memoryless
counterpart (which is a generalized telegraph equation) in order to prove exact
controllability of the viscoelastic body at precisely the same times at which
the telegraph equation is controllable.
  The comparison is done using a moment method approach to controllability and
we prove, using the perturbations theorems of Paley-Wiener and Bari, that a new
sequence derived from the viscoelastic system is a Riesz sequence, a fact that
implies controllability of the viscoelastic system.
  The results so obtained generalize existing controllability results and
furthermore show that the ``sharp'' control time for the telegraph equation and
the viscoelastic system coincide.
