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In view of the case that time-delay arises in the output measurements and the states are not all measurable in practical engineering control, the robust output feedback stabilization problem is investigated for a class of nonlinear time-delay systems in the presence of delayed output measurement. First, based on Lyapunov-Krasovskii functional stability theory, a sufficient condition is given under which the whole system consisting of the original system and the feedback controller with the observer is robust asymptotically stable at the equilibrium, moreover, the feedback gain and the observer gain can be obtained. And then, by employing the result presented, the robust stabilization problem is solved for the hydraulic automatic gauge control (HAGC) system in a cold strip rolling mill. It is shown under the case that the instrumentation used only is the thickness meter, there exists a delay-independent dynamic output feedback robust controller such that the roll gap, the depress force of the hydraulic cylinder and the strip exit thickness all can be regulated to their desired set values regardless of the nonlinearity and uncertainty in the dynamic descriptions of the system as well as the output time-delay in the measurement. Finally, the simulation results are given to show the effectiveness of the proposed control scheme.