  The planar inverted pendulum with a vibrating pivot point in the presence of
an additional horizontal force field is studied. The horizontal force is not
assumed to be small or rapidly oscillating. We assume that the pivot point of
the pendulum rapidly oscillates in the vertical direction and the period of
these oscillations is commensurable with the period of horizontal force. This
system can be considered as a strong generalization of the Kapitza pendulum.
Previously it was shown that for any horizontal force there always exists a
non-falling periodic solution in the considered system. In particular, when
there is no horizontal force, this periodic solution is the vertical upward
position. In the paper we present analytical and numerical results concerning
the existence of asymptotically stable non-falling periodic solutions in the
system.
