  In this paper, we study the exact dynamics of open quantum systems to the
case with periodic driving field. It is shown that different from the static
adjustment of the system on-site energy that can either generate or destroy the
dissipationless localized bound states, the periodic driving can either
preserve the existed localized bound states or destroy some of them but cannot
generate new localized bound states. With the picture of energy transfer
involved with the driving field, we find the condition for the survival of the
localized bound states when the driving amplitude is weak. For the strong
driving case, the condition breaks down because of the strong energy
renormalization to the originally existed localized bound states. These
properties of decoherence dynamics may help in controlling the quantum state
against decoherence for the sake of its sensitivity to the fundamental
frequency of the driving field.
