### Abstract

In this paper, both Euclidean geometric and non-Euclidean geometric descriptions for the regions of the solution set to the covariance partial realization problem are discussed. In particular, it is shown that all the solution functions are located inside a Euclidean disk - the Weyl disk, and a non-Euclidean disk - the Apollonian disk. The radius of each disk depends on the norm of the parameterizing Schur functions. Moreover, it is pointed out that the well known maximum entropy solution is exactly the hyperbolic center of the Apollonian disk; while, the associated power spectral density function is the geometric mean center of the real region where the Wyel disk is projected to along the imaginary axis. Sensitivity analysis of the Weyl disk radius and Apollonian disk center due to the perturbation of the given finite covariance data is presented.

Original language | English (US) |
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Title of host publication | American Control Conference |

Publisher | Publ by IEEE |

Pages | 627-632 |

Number of pages | 6 |

ISBN (Print) | 0780308611, 9780780308619 |

DOIs | |

State | Published - 1993 |

Event | Proceedings of the 1993 American Control Conference Part 3 (of 3) - San Francisco, CA, USA Duration: Jun 2 1993 → Jun 4 1993 |

### Publication series

Name | American Control Conference |
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### Other

Other | Proceedings of the 1993 American Control Conference Part 3 (of 3) |
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City | San Francisco, CA, USA |

Period | 6/2/93 → 6/4/93 |

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## Cite this

*American Control Conference*(pp. 627-632). (American Control Conference). Publ by IEEE. https://doi.org/10.23919/acc.1993.4792934