  We study the large-time behavior of a class of periodically driven
macroscopic systems. We find, for a certain range of the parameters of either
the system or the driving fields, the time-averaged asymptotic behavior
effectively is that of certain other equilibrium systems. We then illustrate
with a few examples how the conventional knowledge of the equilibrium systems
can be made use in choosing the driving fields to engineer new phases and to
induce new phase transitions.
