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We investigate output feedback stabilization for a class of high-order nonlinear systems whose output function and nonlinear terms are unknown. First, a smooth state feedback control law is designed by adding a power integrator technique. Next, we design a high-order observer to estimate the unmeasurable state, and allocate gains of the observer one by one in an iterative way. Finally, a dynamic output compensator is achieved such that the closed-loop system converges to the equilibrium point quick. Two examples are provided to demonstrate the effectiveness of the proposed method.