## Abstract

We derive upper bounds for the McMillan degree of all H^{∞}-optimal controllers associated with design problems which may be embedded in a certain generalized regular configuration. Our analysis is confined to problems of the first kind, which are characterized by the assumption that both P_{12}(s) and P_{21}(s) are square but not necessarily of the same size. This paper, which uses interpolation theory, complements a previous paper which addresses the same problem through an approach based on approximation theory. We demonstrate that the interpolation theory approach is more direct and circumvents a number of the technical difficulties in the previous method: the final outcome is a much shorter proof. As a by-product, we achieve a new result on the degree of an optimal solution of the matrix Nevanlinna-Pick problem.

Original language | English |
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Pages (from-to) | 347-386 |

Number of pages | 40 |

Journal | Linear Algebra and Its Applications |

Volume | 98 |

Issue number | C |

DOIs | |

Publication status | Published - Jan 1988 |

Externally published | Yes |

## ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

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