  We find the conditions under which the spectrum of the unitary time evolution
operator for a periodically rank-N kicked system remains pure point. This
stability result allows one to analyse the onset of, or lack of chaos in this
class of quantum mechanical systems, extending the results for rank-1 systems
produced by Combescure and others. This work includes a number of unitary
theorems equivalent to those well known and used in the self-adjoint theory.
