### Abstract

The transformation of zero coprime system equivalence (z.c.s.e.) with its various characterizations is shown to have at least one important role for two dimensional linear systems theory. This paper shows that it is z.c.s.e. which forms the basis of the generalization of Rosenbrock's characterization of all least order polynomial realizations of a transfer function matrix for the case of 2-D systems. The definition of what consistutes the least order is shown to be crucial.

Original language | English |
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Pages (from-to) | 491-503 |

Number of pages | 13 |

Journal | International Journal of Control |

Volume | 71 |

Issue number | 3 |

Publication status | Published - 1998 |

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### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*International Journal of Control*,

*71*(3), 491-503.

**A transformation for 2-D linear systems and a generalization of a theorem of Rosenbrock.** / Pugh, A. C.; Mcinerney, S. J.; Boudellioua, M. S.; Johnson, D. S.; Hayton, G. E.

Research output: Contribution to journal › Article

*International Journal of Control*, vol. 71, no. 3, pp. 491-503.

}

TY - JOUR

T1 - A transformation for 2-D linear systems and a generalization of a theorem of Rosenbrock

AU - Pugh, A. C.

AU - Mcinerney, S. J.

AU - Boudellioua, M. S.

AU - Johnson, D. S.

AU - Hayton, G. E.

PY - 1998

Y1 - 1998

N2 - The transformation of zero coprime system equivalence (z.c.s.e.) with its various characterizations is shown to have at least one important role for two dimensional linear systems theory. This paper shows that it is z.c.s.e. which forms the basis of the generalization of Rosenbrock's characterization of all least order polynomial realizations of a transfer function matrix for the case of 2-D systems. The definition of what consistutes the least order is shown to be crucial.

AB - The transformation of zero coprime system equivalence (z.c.s.e.) with its various characterizations is shown to have at least one important role for two dimensional linear systems theory. This paper shows that it is z.c.s.e. which forms the basis of the generalization of Rosenbrock's characterization of all least order polynomial realizations of a transfer function matrix for the case of 2-D systems. The definition of what consistutes the least order is shown to be crucial.

UR - http://www.scopus.com/inward/record.url?scp=0032183706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032183706&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032183706

VL - 71

SP - 491

EP - 503

JO - International Journal of Control

JF - International Journal of Control

SN - 0020-7179

IS - 3

ER -