Infinite-dimensional LMI approach to H<sup>∞</sup> control synthesis for linear systems with time delay

Takehito Azuma, Kojiro Ikeda, Kenko Uchida

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


    This paper considers a synthesis problem of H<sup>∞</sup> controllers for linear systems with time delay in the form of delay-dependent memory state feedback, and develops a new Linear Matrix Inequalities (LMIs) approach. First, we present an existence condition and an explicit formula of H<sup>∞</sup> controllers in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay-independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of H<sup>∞</sup> controllers based on the finite-dimensional LMIs.

    Original languageEnglish
    Title of host publicationEuropean Control Conference, ECC 1999 - Conference Proceedings
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Number of pages6
    ISBN (Print)9783952417355
    Publication statusPublished - 2015 Mar 24
    Event1999 European Control Conference, ECC 1999 - Karlsruhe, Germany
    Duration: 1999 Aug 311999 Sept 3


    Other1999 European Control Conference, ECC 1999


    • H<sup>∞</sup> control synthesis problem
    • Linear Matrix Inequalities
    • Memory state feedback controllers
    • Time delay systems

    ASJC Scopus subject areas

    • Control and Systems Engineering


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