The robustness of rank one μ (or called structured singular value) problem with phase-informed uncertainty is studied in this paper. By simple geometric analysis, we develop a procedure to obtain the exact value of phase μ for the rank oneproblem. This result links directly with the Kharitonov-type analysis for a characteristic polynomial with each complex uncertain coefficient lying in a fan-shaped region. It will provide a less conservative robustness evaluation than considering onlynorm bounded information of uncertainty. An algorithm of applying the result to improve the computation of a tight lower bound of general phase μ is also proposed.
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