This paper focused on the control design problem regarding the hydraulic support pushing system, with full consideration of the saturation structure of the control input. With the help of the backstepping technique, some sufficient conditions were established to ensure local exponential stability of the error system between the hydraulic support pushing system and the reference system, simultaneously providing an estimation of the attractive domain. In addition, a potential relationship between the saturation structure and attractive domain was established, which was crucial for achieving local exponential stability in the framework of saturation limitations. It showed that the size of the attractive domain was not only determined by the structure of control input but was also affected by the saturation structure. Finally, some simulations were presented to illustrate the effectiveness of the proposed results.