Hydraulic support is important equipment in the fully mechanized mining face, and the control performance of the hydraulic support multi-cylinder system directly affects the smooth progress of coal mining process, which is the basis for the continuous advancement of the coal face. However, the friction force of the hydraulic support in the process of pulling the frame is complex due to the underground environmental load. Moreover, the parameters of the moving cylinder are uncertain, and the state of the system cannot be fully measured, which increases the difficulty of control. A proportional-integral-derivative controller is usually used in electro-hydraulic closed-loop control systems because of its computational complexity, but its robustness is poorly adapted to variable load conditions in the coal mine. Therefore, a robust output feedback position controller is proposed in this paper to improve control accuracy and system robustness with only position signal. The multi-cylinder system of hydraulic support is modeled as a standard type, and then a high-order differentiator is proposed to estimate the immeasurable system states using the output position signal. A neural network compensator is applied to estimate and compensate for the external disturbance of the moving cylinder. Furthermore, the parameters of the ZY3200/08/18D hydraulic support are adopted to analyze the effectiveness of the designed controller in simulations. Finally, a real-time control system of hydraulic support is built, and the experimental results show that the novel robust output feedback controller has improved by 47.2% and 30.6% in tracking accuracy compared to PI controller.