A dual formulation of mixed μ and on the losslessness of (D,G)-scaling

Gjerrit Meinsma, Yash Shrivastava, Minyue Fu

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    Abstract

    This paper studies the mixed structured singular value, μ, and the well-known (D,G)-scaling upper bound, ν. A dual characterization of μ and ν is derived, which intimately links the two values. Using the duals it is shown that ν is guaranteed to be lossless (i.e. equal to μ) if and only if 2(mr+me)+mC ⩽3, where mr, mc; and mC are the numbers of repeated real scalar blocks, repeated complex scalar blocks, and full complex blocks, respectively. The losslessness result further leads to a variation of the well-known Kalman-Yakubovich-Popov lemma and Lyapunov inequalities.
    Original languageUndefined
    Pages (from-to)1032-1036
    Number of pages5
    JournalIEEE transactions on automatic control
    Volume42
    Issue number7
    DOIs
    Publication statusPublished - 1997

    Keywords

    • mixed structured singular values
    • Linear matrix inequalities
    • METIS-140323
    • Terms-Duality
    • IR-29689
    • Kalman-Yakubovich-Popov lemma

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