  We study many-body localised quantum systems subject to periodic driving. We
find that the presence of a mobility edge anywhere in the spectrum is enough to
lead to delocalisation for any driving strength and frequency. By contrast, for
a fully localised many-body system, a delocalisation transition occurs at a
finite driving frequency. We present numerical studies on a system of
interacting one-dimensional bosons and the quantum random energy model, as well
as simple physical pictures accounting for those results.
