Multiblock problems for almost periodic matrix functions of several variables

Leiba Rodman, Ilya Spitkovsky, Hugo J. Woerdeman

    Research output: Contribution to journalArticle

    Abstract

    In this paper we solve positive and contractive multiblock problems in the Wiener algebra of almost periodic functions of several variables. We thus generalize the classical four block problem that appears in robust control in many ways. The necessary and sufficient conditions are in terms of appropriate Toeplitz (positive case) and Hankel operators (contractive case) on Besikovitch space. In addition, a model matching interpretation is given, and some more general patterns are treated as well.

    Original languageEnglish (US)
    Pages (from-to)117-148
    Number of pages32
    JournalNew York Journal of Mathematics
    Volume7
    StatePublished - Dec 1 2001

    Fingerprint

    Multiblock
    Matrix Function
    Almost Periodic
    Several Variables
    Periodic Functions
    Wiener Algebra
    Almost Periodic Functions
    Model Matching
    Hankel Operator
    Otto Toeplitz
    Robust Control
    Necessary Conditions
    Generalise
    Sufficient Conditions
    Interpretation

    Keywords

    • Almost periodic matrix functions
    • Band method
    • Besikovitch spaces
    • Contractive multiblock extensions
    • Hankel operators
    • Model matching
    • Positive multiblock extensions
    • Toeplitz operators

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Multiblock problems for almost periodic matrix functions of several variables. / Rodman, Leiba; Spitkovsky, Ilya; Woerdeman, Hugo J.

    In: New York Journal of Mathematics, Vol. 7, 01.12.2001, p. 117-148.

    Research output: Contribution to journalArticle

    Rodman, L, Spitkovsky, I & Woerdeman, HJ 2001, 'Multiblock problems for almost periodic matrix functions of several variables', New York Journal of Mathematics, vol. 7, pp. 117-148.
    Rodman, Leiba ; Spitkovsky, Ilya ; Woerdeman, Hugo J. / Multiblock problems for almost periodic matrix functions of several variables. In: New York Journal of Mathematics. 2001 ; Vol. 7. pp. 117-148.
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