The aim of this paper is to design an input sequence for an identification experiment that makes the worst-case \(\nu\)-gap between the identified model and the uncertainty region around it as small as possible, where the worst-case \(\nu\)-gap arises from an optimization of the Vinnicombe \(\nu\)-gap over the uncertainty ellipsoid in a parameter space. The objective of robust controller design is thus to stabilize all plants in the uncertainty region. The experiment design is performed via the input power spectrum optimization. Two cost functions are investigated which represent different levels of trade-off between accuracy and computational complexity. It is shown that the optimization of the input power spectrum with respect to these cost criteria can be reduced to standard numerical algorithms of convex analysis. Simulations show clearly the superiority of the proposed cost functions over other classical design criteria.