Dual LMI approach to H performance limitation analysis of sensitivity and complementary sensitivity functions

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    2 Citations (Scopus)

    Abstract

    In this paper, we study a dual-LMI-based approach to H performance limitation analysis of SISO systems. The scope includes the analysis of the sensitivity function S = (1 + PK)-1 and the complementary sensitivity function T = (1 + PK)-1 PK where P and K stand for the plant and the controller, respectively. The H performance limitations for these transfer functions are well investigated, and exact closed-form performance bounds are already known for the cases where the plant has the sole unstable zero (i.e., non-minimum phase zero) of degree one or the sole unstable pole of degree one. The goal of this paper is to show that such exact bounds can be reproduced by a dual LMI approach. To this end, we study a Lagrange dual of the standard SDP that is usually used to design H optimal controllers by numerical computation. By characterizing the structure of dual feasible solutions in terms of unstable zeros and unstable poles of the plant, we clarify that we can construct an optimal solution for the dual SDP analytically. It follows that we obtain exact H performance bounds that are consistent with the known results.

    Original languageEnglish
    Title of host publication2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016 - Part of 2016 IEEE Multi-Conference on Systems and Control
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages1440-1445
    Number of pages6
    ISBN (Electronic)9781509007592
    DOIs
    Publication statusPublished - Oct 19 2016
    Event2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016 - Buenos Aires, Argentina
    Duration: Sep 19 2016Sep 22 2016

    Publication series

    NameProceedings of the IEEE International Symposium on Computer-Aided Control System Design
    Volume2016-October
    ISSN (Print)2165-3011
    ISSN (Electronic)2165-302X

    Other

    Other2016 IEEE Conference on Computer Aided Control System Design, CACSD 2016
    CountryArgentina
    CityBuenos Aires
    Period9/19/169/22/16

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering
    • Computer Science Applications
    • Control and Optimization

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