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• Propose an input time-delay model to approximate the major effect of valve dynamics. • Propose an ESO-based output feedback controller with valve dynamics compensation. • The closed-loop system stability analysis is completed by using an LK functional. • The effectiveness of the proposed controller is verified via comparative experiments. Valve dynamics play an important role in the high-dynamic tracking performance of hydraulic systems. However, how to effectively compensate them remains an issue. From the frequency-domain analysis, it is recognized that the core effect of valve dynamics is the phase lag within the frequency range of interest. In this paper, a time-delay model which does not increase the entire system order is innovatively proposed to approximate the valve dynamics. As a result, the "explosion of complexity" in the backstepping control could be greatly alleviated. By introducing an auxiliary signal and incorporating a concept of desired-trajectory-based feedforward compensation, a practical output feedback backstepping controller is proposed for the motion control of a hydraulic actuator with integration of a robust delay compensating feedback and an extended state observer (ESO). The constructed ESO provides the estimates of both unmeasurable states and matched uncertainty, which ensures that the proposed controller only uses the output information and improves the system robustness. In addition, the valve dynamics are effectively compensated by the robust delay compensating feedback which contains a finite integral of past control values. The Lyapunov-based closed-loop system stability analysis using a Lyapunov-Krasovskii functional revealed that a uniformly ultimately bounded tracking performance is guaranteed by the proposed controller. Comparative experiments were conducted to verify the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]