### Abstract

Multivariate polynomial matrices arise from the treatment of functional linear systems such as systems described by partial differential equations, delay-differential equations or linear multidimensional discrete equations. In this paper we present conditions under which a class of multivariate polynomial matrices is equivalent to a block diagonal form. The conditions correspond to the decomposition of the associated linear systems of functional equations. The constructive method which can be easily implemented on a computer algebra system is illustrated by an example.

Original language | English |
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Pages (from-to) | 1747-1753 |

Number of pages | 7 |

Journal | Applied Mathematical Sciences |

Issue number | 33-36 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Decomposition
- Equivalence
- Functional systems
- Multivariate polynomial matrices
- Smith form
- Unimodular

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

**On the decoupling of a class of linear functional systems.** / Boudellioua, Mohamed S.

Research output: Contribution to journal › Article

*Applied Mathematical Sciences*, no. 33-36, pp. 1747-1753. https://doi.org/10.12988/ams.2014.42119

}

TY - JOUR

T1 - On the decoupling of a class of linear functional systems

AU - Boudellioua, Mohamed S.

PY - 2014

Y1 - 2014

N2 - Multivariate polynomial matrices arise from the treatment of functional linear systems such as systems described by partial differential equations, delay-differential equations or linear multidimensional discrete equations. In this paper we present conditions under which a class of multivariate polynomial matrices is equivalent to a block diagonal form. The conditions correspond to the decomposition of the associated linear systems of functional equations. The constructive method which can be easily implemented on a computer algebra system is illustrated by an example.

AB - Multivariate polynomial matrices arise from the treatment of functional linear systems such as systems described by partial differential equations, delay-differential equations or linear multidimensional discrete equations. In this paper we present conditions under which a class of multivariate polynomial matrices is equivalent to a block diagonal form. The conditions correspond to the decomposition of the associated linear systems of functional equations. The constructive method which can be easily implemented on a computer algebra system is illustrated by an example.

KW - Decomposition

KW - Equivalence

KW - Functional systems

KW - Multivariate polynomial matrices

KW - Smith form

KW - Unimodular

UR - http://www.scopus.com/inward/record.url?scp=84898923719&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898923719&partnerID=8YFLogxK

U2 - 10.12988/ams.2014.42119

DO - 10.12988/ams.2014.42119

M3 - Article

AN - SCOPUS:84898923719

SP - 1747

EP - 1753

JO - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

SN - 1312-885X

IS - 33-36

ER -