Distance measures, robust stability conditions and robust performance guarantees for uncertain feedback systems

George Papageorgiou, Alexander Lanzon

    Research output: Chapter in Book/Report/Conference proceedingChapter


    Given a nominal plant, a perturbed plant, an uncertainty structure and performance weights, we use robust model validation ideas to define and compute a measure of the distance between the nominal and perturbed plants. We also define a stability margin for a feedback system that is related to robust stability and nominal performance, and derive conditions for the stability and bounds for the performance degradation of the perturbed feedback system in terms of the distance measure. These robust stability and robust performance results give the distance measure a feedback interpretation. The simplicity and power of our procedure for computing the distance between two systems is illustrated using a normalized coprime factor uncertainty model to derive results that have already been published in the literature using different techniques. All systems considered in this paper are linear timeinvariant. Keywords: Robust stability, robust performance, distance measures, model validation, feedback systems, gap metric, ν-gap matric, control, stability margin. © Springer-Verlag Berlin Heidelberg 2006.
    Original languageEnglish
    Title of host publicationLecture Notes in Control and Information Sciences|Lect. Notes Control Inf. Sci.
    Place of PublicationBerlin, Germany
    PublisherSpringer Nature
    Number of pages27
    Publication statusPublished - 16 Mar 2006


    • Distance measures
    • Feedback systems
    • Gap metric
    • H∞ control
    • Model validation
    • Robust performance
    • Robust stability
    • Stability margin
    • V -gap matric


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