  We present a general formulation of Floquet states of periodically
time-dependent open Markovian quasi-free fermionic many-body systems in terms
of a discrete Lyapunov equation. Illustrating the technique, we analyze
periodically kicekd XY spin 1/2 chain which is coupled to a pair of Lindblad
reservoirs at its ends. A complex phase diagram is reported with re-entrant
phases of long range and exponentially decaying spin-spin correlations as some
of the system's parameters are varied. The structure of phase diagram is
reproduced in terms of counting non-trivial stationary points of Floquet
quasi-particle dispersion relation.
