This paper addresses the practically important question of when a nonlinear system can be asymptotically stabilized with a linear proportional-integral (PI) controller, and shows that it is possible if the system can be passified with constant (though unknown) control actions. This simple result is then used to propose a constructive methodology to design PI schemes for switched power converters, which are viewed from a novel perspective: with the switches acting as effective "port variables" that establish a passive mapping with suitably defined outputs. This should be contrasted with the classical viewpoint where the switches regulate the internal energy exchanges. The framework provides also rules to tune the parameters of other linear control schemes to ensure stability. Detailed calculations are given for a three-phase rectifier for which, interestingly, the resulting PI resembles the widely popular active-reactive (PQ) instantaneous power controller of Akagi and co-workers. Experimental results that compare the performance of the proposed PI with various other linear and nonlinear designs are given.