  We show that the correlation functions of a class of periodically driven
integrable closed quantum systems approach their steady state value as
$n^{-(\alpha+1)/\beta}$, where $n$ is the number of drive cycles and $\alpha$
and $\beta$ denote positive integers. We find that generically $\beta=2$ within
a dynamical phase characterized by a fixed $\alpha$; however, its value can
change to $\beta=3$ or $\beta=4$ either at critical drive frequencies
separating two dynamical phases or at special points within a phase. We show
that such decays are realized in both driven Su-Schrieffer-Heeger (SSH) and
one-dimensional (1D) transverse field Ising models, discuss the role of
symmetries of the Floquet spectrum in determining $\beta$, and chart out the
values of $\alpha$ and $\beta$ realized in these models. We analyze the SSH
model for a continuous drive protocol using a Floquet perturbation theory which
provides analytical insight into the behavior of the correlation functions in
terms of its Floquet Hamiltonian. This is supplemented by an exact numerical
study of a similar behavior for the 1D Ising model driven by a square pulse
protocol. For both models, we find a crossover timescale $n_c$ which diverges
at the transition. We also unravel a long-time oscillatory behavior of the
correlators when the critical drive frequency, $\omega_c$, is approached from
below ($\omega < \omega_c$). We tie such behavior to the presence of multiple
stationary points in the Floquet spectrum of these models and provide an
analytic expression for the time period of these oscillations.
