Robustness under Bounded Uncertainty with Phase Information
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We consider uncertain linear systems where the uncertainties, in addition to being bounded, also satisfy constraints on their phase. In this context, we define the ﲰhase-sensitive structured singular value (PS-SSV) of a matrix, and show that sufficient (and sometime 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 to the case where the uncertainties are structured (diagonal or block-diagonal, for instance).