  In this paper, the mathematical framework providing a description of
completely positive and trace preserving dynamics of open quantum systems is
addressed. Special case of time-dependent Lindbladian governed by periodic
Hamiltonian is concerned. It is proven, that appropriate trace preserving
dynamical map of such periodically driven system may be constructed by
application of Floquet theory. Appropriate Lindbladian and Markovian master
equation in weak coupling regime and resulting dynamical map are constructed.
Some examples of application of developed technique are given.
