In this study we formulate H°°oo servo compensator where displacement signals are used as the controlled variables and their time derivatives are used as partial-state feedback signals for stabilizing and positioning control of a cart and inverted flexible pendulum system. The feedback loop of the part of the state variables except the controlled variables is added to the feedback loop of the controlled variables in the design of the H°° compensator. Through this formulation the order of the designed compensator is reduced by the order of the weighting functions for the time derivative signals. By numerical calculations and experiments, we investigate the settling characteristics and the robust stability against a disturbance to the pendulum with two kinds of controllers, the output feedback controller by the displacement feedback and the output feedback controller adding the cart velocity feedback. It is shown that although the displacement-output feedback controller has a big overshoot in the step response and the positioning of the cart is difficult, by means of the partial-state feedback controller with a cart velocity feedback the overshoot can be reduced and stable positioning control of the cart is possible. Also it is verified that the servo compensator is superior to the regulator-based compensator in the settling characteristics.