Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems

Kojiro Ikeda, Takehito Azuma, Kenko Uchida

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of L2 gain of closed loop systems, 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 controllers based on the finite-dimensional LMIs.

    Original languageEnglish
    Pages (from-to)505-520
    Number of pages16
    JournalKybernetika
    Volume37
    Issue number4
    Publication statusPublished - 2001

    Fingerprint

    Time-delay Systems
    Linear matrix inequalities
    Matrix Inequality
    Linear Time
    Linear Inequalities
    Time delay
    Linear Systems
    Synthesis
    Controller
    Controllers
    Data storage equipment
    Delay-dependent
    State feedback
    State Feedback
    Closed loop systems
    Closed-loop System
    Dimensionality
    Explicit Formula
    Infinity
    Cover

    ASJC Scopus subject areas

    • Human-Computer Interaction
    • Control and Systems Engineering

    Cite this

    Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems. / Ikeda, Kojiro; Azuma, Takehito; Uchida, Kenko.

    In: Kybernetika, Vol. 37, No. 4, 2001, p. 505-520.

    Research output: Contribution to journalArticle

    Ikeda, Kojiro ; Azuma, Takehito ; Uchida, Kenko. / Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems. In: Kybernetika. 2001 ; Vol. 37, No. 4. pp. 505-520.
    @article{d0d5ac456f874033b6ab6ab12c3e315b,
    title = "Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems",
    abstract = "This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of L2 gain of closed loop systems, 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 controllers based on the finite-dimensional LMIs.",
    author = "Kojiro Ikeda and Takehito Azuma and Kenko Uchida",
    year = "2001",
    language = "English",
    volume = "37",
    pages = "505--520",
    journal = "Kybernetika",
    issn = "0023-5954",
    publisher = "Academy of Sciences of the Czech Republic",
    number = "4",

    }

    TY - JOUR

    T1 - Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems

    AU - Ikeda, Kojiro

    AU - Azuma, Takehito

    AU - Uchida, Kenko

    PY - 2001

    Y1 - 2001

    N2 - This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of L2 gain of closed loop systems, 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 controllers based on the finite-dimensional LMIs.

    AB - This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of L2 gain of closed loop systems, 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 controllers based on the finite-dimensional LMIs.

    UR - http://www.scopus.com/inward/record.url?scp=0035648514&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0035648514&partnerID=8YFLogxK

    M3 - Article

    VL - 37

    SP - 505

    EP - 520

    JO - Kybernetika

    JF - Kybernetika

    SN - 0023-5954

    IS - 4

    ER -