A geometrical formulation of the μ-lower bound problem

Jongrae Kim, Declan Bates, Ian Postlethwaite

    Research output: Contribution to journalArticlepeer-review

    13 Citations (Scopus)


    A new problem formulation for the structured singular value μ in the case of purely real (possibly repeated) uncertainties is presented. The approach is based on a geometrical interpretation of the singularity constraint arising in the μ lower bound problem. An interesting feature of this problem formulation is that the resulting parametric search space is independent of the number of times any parameter is repeated in the structured uncertainty matrix. A corresponding lower bound algorithm combining randomisation and optimisation methods is developed, and some probabilistic performance guarantees are derived. The potential usefulness of the proposed approach is demonstrated on two high-order real μ analysis problems from the aerospace and systems biology literature
    Original languageEnglish
    Pages (from-to)465-472
    JournalIET Control Theory & Applications
    Issue number4
    Publication statusPublished - 2009


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