### Abstract

We present an algebraic method to compute a globally optimal H2 approximation of order N-3 to a given system of order N. First, the problem is formulated as a two-parameter polynomial eigenvalue problem with a special structure. To solve it, we apply and generalize algebraic techniques used in the computation of the Kronecker canonical form of a matrix pencil. Finiteness of the number of nontrivial solutions then allows the problem to be reduced to a one-parameter polynomial eigenvalue problem, which is solved with standard numerical methods. An example demonstrates the approach and provides a proof of principle.

Original language | English |
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Title of host publication | System Identification, the 16th IFAC Symposium on System Identification |

Pages | 704-709 |

Volume | 45 |

DOIs | |

Publication status | Published - 1 Jan 2012 |

Event | 16th IFAC Symposium on System Identification - Duration: 11 Jul 2012 → 13 Jul 2012 |

### Conference

Conference | 16th IFAC Symposium on System Identification |
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Period | 11/07/12 → 13/07/12 |

## Cite this

Peeters, R. L. M., Bleylevens, I. W. M., & Hanzon, B. (2012). On Algebraic and Linear Algebraic Aspects of Co-Order Three H2 Model Order Reduction. In

*System Identification, the 16th IFAC Symposium on System Identification*(Vol. 45, pp. 704-709) https://doi.org/10.3182/20120711-3-BE-2027.00379