Multiblock problems for almost periodic matrix functions of several variables

Leiba Rodman; Ilya M. Spitkovsky; Hugo J. Woerdeman

Multiblock problems for almost periodic matrix functions of several variables

Leiba Rodman, Ilya M. Spitkovsky, Hugo J. Woerdeman

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	117-148
Number of pages	32
Journal	New York Journal of Mathematics
Volume	7
State	Published - 2001

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

General Mathematics

Cite this

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title = "Multiblock problems for almost periodic matrix functions of several variables",

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.",

keywords = "Almost periodic matrix functions, Band method, Besikovitch spaces, Contractive multiblock extensions, Hankel operators, Model matching, Positive multiblock extensions, Toeplitz operators",

author = "Leiba Rodman and Spitkovsky, {Ilya M.} and Woerdeman, {Hugo J.}",

year = "2001",

language = "English (US)",

volume = "7",

pages = "117--148",

journal = "New York Journal of Mathematics",

issn = "1076-9803",

publisher = "University at Albany",

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T1 - Multiblock problems for almost periodic matrix functions of several variables

AU - Rodman, Leiba

AU - Spitkovsky, Ilya M.

AU - Woerdeman, Hugo J.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - Almost periodic matrix functions

KW - Band method

KW - Besikovitch spaces

KW - Contractive multiblock extensions

KW - Hankel operators

KW - Model matching

KW - Positive multiblock extensions

KW - Toeplitz operators

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M3 - Article

AN - SCOPUS:0142225504

SN - 1076-9803

VL - 7

SP - 117

EP - 148

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

ER -

Multiblock problems for almost periodic matrix functions of several variables

Abstract

Keywords

ASJC Scopus subject areas

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