### Abstract

Based on the matrix fraction descriptions of multi-variable control systems, this paper presents the generalized matrix Euclidean algorithms for solving Diophantine equations and associated problems. A chain rule is developed for finding the greatest common right(left) divisor of two square(non-square) polynomial matrices and the irreducible right(left) matrix fraction description from the reducible or irreducible left(right) matrix fraction description. Also, the development of multi-variable pole-assignment controllers are discussed for engineering applications.

Original language | English |
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Pages (from-to) | 55-72 |

Number of pages | 18 |

Journal | Computers and Mathematics with Applications |

Volume | 25 |

Issue number | 12 |

DOIs | |

Publication status | Published - 1993 Jan 1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computers and Mathematics with Applications*,

*25*(12), 55-72. https://doi.org/10.1016/0898-1221(93)90186-Y

}

*Computers and Mathematics with Applications*, vol. 25, no. 12, pp. 55-72. https://doi.org/10.1016/0898-1221(93)90186-Y

**Generalized matrix Euclidean algorithms for solving diophantine equations and associated problems.** / Tsai, Jason Sheng-Hon; Chen, S. S.; Shieh, L. S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Generalized matrix Euclidean algorithms for solving diophantine equations and associated problems

AU - Tsai, Jason Sheng-Hon

AU - Chen, S. S.

AU - Shieh, L. S.

PY - 1993/1/1

Y1 - 1993/1/1

N2 - Based on the matrix fraction descriptions of multi-variable control systems, this paper presents the generalized matrix Euclidean algorithms for solving Diophantine equations and associated problems. A chain rule is developed for finding the greatest common right(left) divisor of two square(non-square) polynomial matrices and the irreducible right(left) matrix fraction description from the reducible or irreducible left(right) matrix fraction description. Also, the development of multi-variable pole-assignment controllers are discussed for engineering applications.

AB - Based on the matrix fraction descriptions of multi-variable control systems, this paper presents the generalized matrix Euclidean algorithms for solving Diophantine equations and associated problems. A chain rule is developed for finding the greatest common right(left) divisor of two square(non-square) polynomial matrices and the irreducible right(left) matrix fraction description from the reducible or irreducible left(right) matrix fraction description. Also, the development of multi-variable pole-assignment controllers are discussed for engineering applications.

UR - http://www.scopus.com/inward/record.url?scp=38249002639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249002639&partnerID=8YFLogxK

U2 - 10.1016/0898-1221(93)90186-Y

DO - 10.1016/0898-1221(93)90186-Y

M3 - Article

AN - SCOPUS:38249002639

VL - 25

SP - 55

EP - 72

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 12

ER -