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

Kojiro Ikeda*, Takehito Azuma, Kenko Uchida

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    20 Citations (Scopus)


    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
    Issue number4
    Publication statusPublished - 2001

    ASJC Scopus subject areas

    • Human-Computer Interaction
    • Control and Systems Engineering


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