Balancing act 2

We have a pendulum made of a rigid, massless rod of length $l$ and a small ball of mass $m$ attached to the end of the rod. The period of small amplitude oscillations is $T_0= 2 \pi \sqrt{\frac lg}$ .

The pivot point (axis of rotation) of the pendulum is not fixed, but it is attached to a mechanism that shakes the pivot point in the vertical directions with amplitude $a\ll l$ and period $T\ll T_0$ . (For $a=0$ we get back the traditional pendulum.)

We set up the rod such that it is in the vertical, unstable position with the ball right above the pivot point. When $a=0,$ this position is unstable; for any small error in positioning the ball, the pendulum will turn over.

Is it possible that if we switch on the shaking $a\ne 0,$ the position becomes stable and the ball will remain over the pivot point indefinitely?