As stated in the introduction of the paper the objective is to maintain the pendulum in the unstable upright position and balance it when it is almost there, even in presence of small perturbations (in a range of ±lO° for the pendulum angle displacement a).When the RIP system is disturbed from the balance state and the pendulum is deviated from the upright position to certain degrees larger than the threshold value, a certain criterion should switch back the system to the swing up control. The swing-up control system which has the goal to bring the pendulum from the stable downward position in the upright position is not treated here. So, the switching process between the swing-up problem and balance control which is done usually by a third controller is not required here.