Minimal positive realizations: a survey of recent results and open problems

Luca Benvenuti; Lorenzo Farina

Kybernetika (2003)

  • Volume: 39, Issue: 2, page [217]-228
  • ISSN: 0023-5954

Abstract

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In this survey paper some recent results on the minimality problem for positive realizations are discussed. In particular, it is firstly shown, by means of some examples, that the minimal dimension of a positive realization of a given transfer function, may be much “larger” than its McMillan degree. Then, necessary and sufficient conditions for the minimality of a given positive realization in terms of positive factorization of the Hankel matrix are given. Finally, necessary and sufficient conditions for a third order transfer function with distinct real positive poles to have a third order positive realization are provided and some open problems related to minimality are discussed.

How to cite

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Benvenuti, Luca, and Farina, Lorenzo. "Minimal positive realizations: a survey of recent results and open problems." Kybernetika 39.2 (2003): [217]-228. <http://eudml.org/doc/33636>.

@article{Benvenuti2003,
abstract = {In this survey paper some recent results on the minimality problem for positive realizations are discussed. In particular, it is firstly shown, by means of some examples, that the minimal dimension of a positive realization of a given transfer function, may be much “larger” than its McMillan degree. Then, necessary and sufficient conditions for the minimality of a given positive realization in terms of positive factorization of the Hankel matrix are given. Finally, necessary and sufficient conditions for a third order transfer function with distinct real positive poles to have a third order positive realization are provided and some open problems related to minimality are discussed.},
author = {Benvenuti, Luca, Farina, Lorenzo},
journal = {Kybernetika},
keywords = {positive systems; positiverealizations; positive system; positive realization},
language = {eng},
number = {2},
pages = {[217]-228},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Minimal positive realizations: a survey of recent results and open problems},
url = {http://eudml.org/doc/33636},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Benvenuti, Luca
AU - Farina, Lorenzo
TI - Minimal positive realizations: a survey of recent results and open problems
JO - Kybernetika
PY - 2003
PB - Institute of Information Theory and Automation AS CR
VL - 39
IS - 2
SP - [217]
EP - 228
AB - In this survey paper some recent results on the minimality problem for positive realizations are discussed. In particular, it is firstly shown, by means of some examples, that the minimal dimension of a positive realization of a given transfer function, may be much “larger” than its McMillan degree. Then, necessary and sufficient conditions for the minimality of a given positive realization in terms of positive factorization of the Hankel matrix are given. Finally, necessary and sufficient conditions for a third order transfer function with distinct real positive poles to have a third order positive realization are provided and some open problems related to minimality are discussed.
LA - eng
KW - positive systems; positiverealizations; positive system; positive realization
UR - http://eudml.org/doc/33636
ER -

References

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