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Mixed One-and Two-Sided Real Uncertainty: A Vertex Result

This note deals with the robustness margin of generalized stability for a parametrized family of real matrices in the case when some of the parameters are known to be no larger (or no smaller) than their nominal value ("one-sided uncertainty"). It is observed that this robustness margin can be computed in terms of a modified structured singular value, with or without frequency sweep. Whether or not one-sided uncertainty is present, if a certain multiaffineness condition is satisfied, a vertex result holds.