## Abstract

Rectangular matrix pencils arise in many contexts in Linear Control Theory, for example the PBH Test for Controllability and the computation of transmission zeros. In this paper, we examine a method to find the distance from an arbitrary given pencil to a nearby rank-deficient one, in light of the fact that rectangular pencils are generically full-rank. We propose an experimental computational method that exhibits quadratic convergence to a local minimum of this distance function. This partially answers the question of the existence of a rank-deficient pencil in a neighborhood of a given pencil. We use the Algorithm to illustrate some limitations of previous algorithms to measure this distance.

Original language | English (US) |
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Pages (from-to) | 207-214 |

Number of pages | 8 |

Journal | Systems and Control Letters |

Volume | 9 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1987 |

### Bibliographical note

Funding Information:* This research was partially supported by NSF Grants DCR-8420935 and DCR-8519029.

## Keywords

- Algebraic structure
- Genericity
- Matrix pencils
- Numerical methods
- Rank-deficiency