## Abstract

In the perturbation theory of linear descriptor systems, it is well known that the theory of eigenvalues and eigenvectors of regular homogeneous matrix pencils is complicated by the fact that arbitrarily small perturbations of the pencil can cause them to disappear. In this paper, the perturbation theory of complex Weierstrass canonical form for regular matrix pencils is investigated. Moreover, since there are applications such that the eigenvalues and eigenvectors do not disappear upon by arbitrarily small perturbations, expressions for the relative error of F_{w} and G_{w}, i.e., ∥ (F + E_{1})_{w} - F_{w} ∥ / ∥ F _{w} ∥ and ∥ (G + E_{2})_{w} - G_{w} ∥ / ∥ G_{w} ∥ are provided by using the Frobenius norm ∥ ∥.

Original language | English |
---|---|

Pages (from-to) | 5-13 |

Number of pages | 9 |

Journal | Systems Science |

Volume | 35 |

Issue number | 4 |

Publication status | Published - 2009 |

Externally published | Yes |

## Keywords

- Complex weierstrass canonical form
- Linear systems
- Perturbation theory