H∞ performance limitations analysis for SISO systems: A dual LMI approach

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    4 Citations (Scopus)

    Abstract

    In a very recent study by the first author and his colleagues, a novel LMI-based approach has been proposed to the best achievable H∞ performance limitations analysis for continuous-time SISO systems. Denoting by P and K a plant and a controller, respectively, and assuming that the plant P has an unstable zero, it was shown that a lower bound of the best achievable H∞ performance with respect to the transfer function (1+PK)-1P can be given analytically in terms of the real part of the unstable zero and the first non-zero coefficient of the Taylor expansion of P around the unstable zero. The goal of this paper is to show that, if the plant P has no unstable zeros except for the sole real unstable zero of degree one, then the lower bound shown there is exact. The exactness proof relies on the detailed analysis on the Lagrange dual problem of the SDP characterizing H∞ optimal controllers. More precisely, we show that we can construct an optimal dual solution proving the exactness analytically in terms of the state-space matrices of the plant P and the unstable zero. This analytical expression of the dual optimal solution is also a main result of this study.

    Original languageEnglish
    Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages6629-6634
    Number of pages6
    ISBN (Electronic)9781479978861
    DOIs
    Publication statusPublished - Feb 8 2015
    Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
    Duration: Dec 15 2015Dec 18 2015

    Publication series

    NameProceedings of the IEEE Conference on Decision and Control
    Volume54rd IEEE Conference on Decision and Control,CDC 2015
    ISSN (Print)0743-1546

    Other

    Other54th IEEE Conference on Decision and Control, CDC 2015
    CountryJapan
    CityOsaka
    Period12/15/1512/18/15

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering
    • Modelling and Simulation
    • Control and Optimization

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