Robustness under bounded uncertainty with phase information

The authors consider uncertain linear systems where the uncertainties, in a ddition to being bounded, also satisfy constraints on their phase, In this context, the authors define the "phase-sensitive structured singular value" (PS-SSV) of a matrix and show that sufficient (and sometimes necessary) co nditions for stability of such uncertain linear systems can be rewritten as conditions involving PS-SSV. They then derive upper bounds for PS-SSV, com putable via convex optimization. They extend these results to the case wher e the uncertainties are structured (diagonal or block-diagonal, for instanc e).