This paper discusses the reduction of the amount of transmitted information for the efficient use of frequency resources in wireless feedback control systems, and clarify the effect of the reduction of the amount of transmitted information. As a typical example of the underactuated controlled object, a rotary inverted pendulum is considered. We propose a reduction method for state information fed back from the controller to the controlled object. It estimates angle or velocity state from the previous state. In addition, we propose a reduction method that temporally omits less important control information and state information. Numerical examples clarify the effect of the reduction methods on the control quality. And we show that the reduction methods achieve large reduction of the amount of transmitted information with small disadvantage of the control quality.