The outdoor antenna servo system is subject to has significant torque disturbances from wind pressures and gusts on the antenna structures, as well as bearing and aerodynamic frictions. This control system should provide a sharp directivity in spite of the environmental disturbances and internal uncertainties. Therefore, the implementation of a real-time controller is necessary for the precise generation of the reference signal and robust tracking performance. In this paper, the discrete-time controller for the quick tracking of a target communication satellite is designed by applying the sampled-data $H_{infty}$ control theory along with the reference signal generated by an improved conventional step-tracking algorithm. The sampled-data $H_{infty}$controller demonstrates superior robustness for the longer sampling period when compared with a simple PID controller.