We present a new approach to parametric robust controller design, where we compute controllers of arbitrary order and structure which minimize the worst-case H-infinity norm over a pre-specified set of uncertain parameters. At the core of our method is a nonsmooth minimization method tailored to functions which are semi-infinite minima of smooth functions. A rich test bench and a more detailed example illustrate the potential of the technique, which can deal with complex problems involving multiple possibly repeated uncertain parameters.