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Abst ract We consider uncertain linear systems where the uncertainties, in addition to being bounded, also satisfy constraints on their phase. In this context, we de ne the \phase-sensitive structured singular value" (PS-SSV) of a matrix, and show that su cient (and sometimes necessary) conditions for stability of such uncertain linear systems can be rewritten as conditions involving PS-SSV. We then derive upper bounds for PS-SSV, computable via convex optimization. We extend these results todoi:10.1109/9.739067 fatcat:x3cctzycrnglnp2nrz4ytfxfte