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In this paper, a dynamic-neural-networks-based adaptive output feedback controller for a class of unknown nonlinear systems is developed under the constraint that only the system output is available for measurement. A model-free state observer is utilized to estimate the system states. Moreover, the effect of network modeling error is also discussed. By means of a Lyapunov method and a matrix Riccati equation, it has been shown that the output feedback control law and weight update laws provide robust stability for the closed-loop system, and guarantee that all signals involved are bounded and the system output tracking error is uniformly ultimately bounded.