  This paper deals with the stability of linear periodic difference delay
systems, where the value at time $t$ of a solution is a linear combination with
periodic coefficients of its values at finitely many delayed instants
$t-\tau_1,\ldots,t-\tau_N$. We establish a necessary and sufficient condition
for exponential stability of such systems when the coefficients have
H\"older-continuous derivative, that generalizes the one obtained for
difference delay systems with constant coefficients by Henry and Hale in the
1970s. This condition may be construed as analyticity, in a half plane, of the
(operator valued) harmonic transfer function of an associated linear control
system.
