  Manipulating the global $PT$ symmetry of a non-Hermitian composite system is
a rather significative and challenging task. Here, we investigate Floquet
control of global $PT$ symmetry in 2D arrays of quadrimer waveguides with
transverse periodic structure along $x$-axis and longitudinal periodic
modulation along $z$-axis. For unmodulated case with inhomogeneous inter- and
intra- quadrimer coupling strength $\kappa_1\neq\kappa$, in addition to
conventional global $PT$-symmetric phase and $PT$-symmetry-breaking phase, we
find that there is exotic phase where global $PT$ symmetry is broken under open
boundary condition, whereas it still is unbroken under periodical boundary
condition. The boundary of phase is analytically given as
$\kappa_1\geq\kappa+\sqrt{2}$ and $1\leq\gamma\leq2$, where there exists a pair
of zero-energy edge states with purely imaginary energy eigenvalues localized
at the left boundary, whereas other $4N-2$ eigenvalues are real. Especially,
the domain of the exotic phase can be manipulated narrow and even disappeared
by tuning modulation parameter. More interestingly, whether or not the array
has initial global $PT$ symmetry, periodic modulation not only can restore the
broken global $PT$ symmetry, but also can control it by tuning modulation
amplitude. Therefore, the global property of transverse periodic structure of
such a 2D array can be manipulated by only tuning modulation amplitude of
longitudinal periodic modulation.
