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This paper considers the quantized output feedback control design for a class of uncertain nonlinear systems. Different from the literature , the nonlinear growth of the systems under investigation depends on the unmeasured states, which makes the observer design in  inapplicable, and renders the performance analysis for the closed-loop system more complex and difficult. First, a new high-gain observer is introduced to reconstruct the unmeasured states. Then, by applying the set-valued maps and recursive control design method in , a quantized output feedback controller is designed. Lastly, by the cyclic-small-gain theorem and dynamic quantization strategy, a sufficient condition is given to guarantee that all states of the closed-loop system are bounded and furthermore output can be ultimately arbitrarily small.