### 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) |
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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

- Mathematics(all)

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## Cite this

Rodman, L., Spitkovsky, I. M., & Woerdeman, H. J. (2001). Multiblock problems for almost periodic matrix functions of several variables.

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