  By directly using the probability formulas of quantum trajectories, we
construct an auxiliary open quantum system for a periodically driven open
quantum system whose dynamics is governed by the Floquet quantum master
equation. This auxiliary system can generate a quantum trajectory ensemble that
is consistent with the canonical quantum trajectory ensemble. We find that, at
a long time limit, though the Lindblad operators are modified, the coherent
dynamics of the auxiliary system is the same as that of the original system. A
periodically driven two-level quantum system is used to illustrate this
construction.
