  We consider a strongly driven two-level (spin) system, with a periodic
external field that induces a sequence of avoided level crossings. The spin
system interacts with a bosonic reservoir which leads to decoherence. A
Markovian dynamical equation is introduced without relying on the rotating wave
approximation in the system-external field interaction. We show that the time
evolution of the two-level system is directed towards an incoherent sum of
periodic Floquet states regardless of the initial state and even the type of
the coupling to the environment. Analyzing the time scale of approaching these
time-dependent pointer states, information can be deduced concerning the nature
and strength of the system-environment coupling. The inversion as a function of
the external field is usually multi-valued, and the form of these hysteresis
curves is qualitatively different for low and high temperatures. For moderate
temperatures we found that the series of Landau-Zener-St\"{u}ckelberg-type
transitions still can be used for state preparation, regardless of the
decoherence rate. Possible applications include quantum information processing
and molecular nanomagnets.
