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

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