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The paper presents a new approach to the robust Hinfin control of an uncertain system via an output feedback controller which is both stable and positive real. The uncertain systems under consideration contain structured uncertainty described by integral quadratic constraints. The controller is designed to achieve absolute stabilization with a specified level of disturbance attenuation. The main result involves solving a state feedback version of the problem by solving an algebraic Riccati equation dependent on a set of scaling parameters. Then two further algebraic Riccati equations are solved which depend on a further set of scaling parameters. The required controller is constructed from the Riccati solutions.