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We are considering the problem of controlling filtered AC/DC switched power converters of the boost type. The control objectives are twofold: 1) guaranteeing a regulated voltage for the supplied load and 2) enforcing power factor correction (PFC) with respect to the main supply network. The considered problem is dealt with using a double-loop controller developed on the basis of the system nonlinear model. The inner-loop is designed by the backstepping technique to cope with the PFC issue. The outer-loop is designed to regulate the converter output voltage. Experimental tests show that the proposed controller actually meets the objectives it is designed for. While similar performances have been experimentally demonstrated, for different converters and controllers, it is the first time that a complete and rigorous formal analysis, based on averaging theory, is developed to describe the observed performances (PFC and output voltage ripples). As a matter of fact, the averaging theory constitutes the natural framework to analyzing the performances due to the periodic nature of the system input signals.