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Five-Full-Block Structured Singular Values of Real Matrices Equal Their Upper Bounds

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arxiv 2007.05222 v2 pith:CCNSNRZ2 submitted 2020-07-10 math.OC

classification math.OC
keywords blocksrealsingularstructureduncertaintyupperapproachbound
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We show that the structured singular value of a real matrix with respect to five full complex uncertainty blocks equals its convex upper bound. This is done by formulating the equality conditions as a feasibility SDP and invoking a result on the existence of a low-rank solution. A counterexample is given for the case of six uncertainty blocks. Known results are also revisited using the proposed approach.

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