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This paper studies the problem of global stabilization by output feedback for a family of uncertain nonlinear systems without zero dynamics. These nonlinear systems are dominated by a triangular system satisfying polynomial growth in the unmeasurable states. The novelty of this paper is that a universal-type adaptive output feedback controller is numerically constructed by using a sum of squares (SOS) optimization algorithm, which can globally regulate all the states of the uncertain systems without knowing the growth rate. An example is presented to show the effectiveness of this methodology.