  We give a partial review of what is known so far on stability of periodically
driven quantum systems versus regularity of the bounded driven force. In
particular we emphasize the fact that unbounded degeneracies of the unperturbed
Hamiltonian are allowed. Then we give a detailed description of an extension to
some unbounded driven forces. This is done by representing the Schroedinger
equation in the instantaneous basis of the time dependent Hamiltonian with a
method that we call progressive diagonalization.
