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In this paper, we provide the synthesis of nonfragile H∞ output feedback controllers which is also optimal with respect to a H∞-norm performance index. The uncertainties are assumed to be polytopic, both in the controller gains and the system dynamics. The sufficient condition of controller existence, the design method of robust and nonfragile H∞ output feedback controller, and the region of controllers which satisfies nonfragility are presented. Also using some change of variables and Schur complements, the obtained sufficient condition can be rewritten as parameterized LMIs, that is, LMIs whose coefficients are functions of a parameter confined to a compact set. A numerical example is presented to demonstrate the efficiency of this method, and the obtained controller guarantees the asymptotic stability and disturbance attenuation of the closed loop system with respect to the uncertainties in the plant and the controller within a resulted polytopic region.