## Abstract

In this paper new algorithms are developed for J-spectral factorization of polynomial matrices. These algorithms are based on the calculus of two-variable polynomial matrices and associated quadratic differential forms, and share the common feature that the problem is lifted from the original one-variable polynomial context to a two-variable polynomial context. The problem of polynomial J-spectral factorization is thus reduced to a problem of factoring a constant matrix obtained from the coefficient matrices of the polynomial matrix to be factored. In the second part of the paper, we specifically address the problem of computing polynomial J-spectral factors in the context of H-infinity control. For this, we propose an algorithm that uses the notion of a Pick matrix associated with a given two-variable polynomial matrix.

Original language | English |
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Pages (from-to) | 24-61 |

Number of pages | 38 |

Journal | Mathematics of Control Signals and Systems |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1999 |

## Keywords

- polynomial J-spectral factorization
- two-variable polynomial matrix
- quadratic differential form
- dissipativity
- Pick matrix