## Abstract

We examine the concept of skew-primeness of polynomial matrices in terms of the associated polynomial model. It is shown that skew-primeness can be characterized in terms of the property of decomposition of a vector space relative to an endomorphism. This basic result is then applied to the special case of nonsingular polynomial matrices. We investigate the nonuniqueness of skew-complements of a skew-prime pair. It is shown that the space of equivalence classes of skew-complements is in bijective correspondence with a finite-dimensional linear space. Finally, the equivalence of the solutions to the problem of output regulation with internal stability obtained via geometric methods and via polynomial matrix techniques is shown explicitly.

Original language | English (US) |
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Pages (from-to) | 403-435 |

Number of pages | 33 |

Journal | Linear Algebra and Its Applications |

Volume | 50 |

Issue number | C |

DOIs | |

State | Published - Apr 1983 |

### Bibliographical note

Funding Information:*This research was supportedi n part by US Army Research Grant DAAG2981-K-0136 and US Air Force Grant AFOSR816238 through the Center for Mathematical System Theory, University of Florida, Gainesville, Florida 32611. ‘This author is with the Department of Electrical Engineering, Gainesville, FL 32611. “Supported in part by the Scientific and Technical Research Council of Turkey.