A test for stability robustness of linear time-varying systems utilizing the linear time-invariant νν-gap; metric

Wynita M. Griggs, Alexander Lanzon, Brian D O Anderson

    Research output: Contribution to journalArticlepeer-review

    Abstract

    A stability robustness test is developed for internally stable, nominal, linear time-invariant (LTI) feedback systems subject to structured, linear time-varying uncertainty. There exists (in the literature) a necessary and sufficient structured small gain condition that determines robust stability in such cases. In this paper, the structured small gain theorem is utilized to formulate a (sufficient) stability robustness condition in a scaled LTI νν-gap; metric framework. The scaled LTI νν-gap; metric stability condition is shown to be computable via linear matrix inequality techniques, similar to the structured small gain condition. Apart from a comparison with a generalized robust stability margin as the final part of the stability test, however, the solution algorithm implemented to test the scaled LTI νν-gap; metric stability robustness condition is shown to be independent of knowledge about the controller transfer function (as opposed to the LMI feasibility problem associated with the scaled small gain condition which is dependent on knowledge about the controller). Thus, given a nominal plant and a structured uncertainty set, the stability robustness condition presented in this paper provides a single constraint on a controller (in terms of a large enough generalized robust stability margin) that (sufficiently) guarantees to stabilize all plants in the uncertainty set. © 2008 John Wiley & Sons, Ltd.
    Original languageEnglish
    Pages (from-to)986-1015
    Number of pages29
    JournalInternational Journal of Robust and Nonlinear Control
    Volume19
    Issue number9
    DOIs
    Publication statusPublished - Jun 2009

    Keywords

    • νν-gap; metric
    • Linear time-varying uncertainty
    • Stability robustness
    • Structured uncertainty

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