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We study the problem of designing the controllers that are robust with respect to the parametric uncertainty. In Part I ?The RankOne Problem? we consider the class of systems with restriction that the structure of uncertainty is limited to a vector. We extend the class of the allowed systems. The main result is the canonical parametrization of all destabilizing uncertainties. We also present a method of obtaining the suboptimal controller of lower order that provides the stability margin as close to the optimal one as we wish. We propose a numerical algorithm for the optimal robust control synthesis. In the special case, when the uncertainty parameter is realvalued, we show that the initial problem can be considered as finitedimensional in the space of variables (semiinfinite convex programming). Part II ?Convex Duality: Matrix Case? generalizes the results to the systems with matrix uncertainties.
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