### 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 - Dec 1 2001 |

### Fingerprint

### 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

*New York Journal of Mathematics*,

*7*, 117-148.

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

Research output: Contribution to journal › Article

*New York Journal of Mathematics*, vol. 7, pp. 117-148.

}

TY - JOUR

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

AU - Rodman, Leiba

AU - Spitkovsky, Ilya

AU - Woerdeman, Hugo J.

PY - 2001/12/1

Y1 - 2001/12/1

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

UR - http://www.scopus.com/inward/record.url?scp=0142225504&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0142225504&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 117

EP - 148

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

SN - 1076-9803

ER -