### Abstract

In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fomasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.

Original language | English |
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Pages (from-to) | 175-181 |

Number of pages | 7 |

Journal | International Journal of Applied Mathematics and Computer Science |

Volume | 16 |

Issue number | 2 |

Publication status | Published - 2006 |

### Fingerprint

### Keywords

- 2-D singular systems
- Invariant polynomials
- Invariant zeros
- Matrix pencils
- Zero-Coprime-Equivalence

### ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Engineering (miscellaneous)
- Applied Mathematics

### Cite this

**An equivalent matrix pencil for bivariate polynomial matrices.** / Boudellioua, Mohamed S.

Research output: Contribution to journal › Article

*International Journal of Applied Mathematics and Computer Science*, vol. 16, no. 2, pp. 175-181.

}

TY - JOUR

T1 - An equivalent matrix pencil for bivariate polynomial matrices

AU - Boudellioua, Mohamed S.

PY - 2006

Y1 - 2006

N2 - In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fomasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.

AB - In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fomasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.

KW - 2-D singular systems

KW - Invariant polynomials

KW - Invariant zeros

KW - Matrix pencils

KW - Zero-Coprime-Equivalence

UR - http://www.scopus.com/inward/record.url?scp=33745468546&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745468546&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 175

EP - 181

JO - International Journal of Applied Mathematics and Computer Science

JF - International Journal of Applied Mathematics and Computer Science

SN - 1641-876X

IS - 2

ER -