Geodesic
Minimal positive realizations: a survey of recent results and open problems
Kybernetika, Tome 39 (2003) no. 2, p. [217].

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 06F05, 93B15, 93B27
Keywords: positive systems; positiverealizations 
@article{KYB_2003__39_2_a10,
     author = {Benvenuti, Luca and Farina, Lorenzo},
     title = {Minimal positive realizations: a survey of recent results and open problems},
     journal = {Kybernetika},
     pages = {[217]},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {2003},
     mrnumber = {1996559},
     zbl = {1249.93036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003__39_2_a10/}
}
TY  - JOUR
AU  - Benvenuti, Luca
AU  - Farina, Lorenzo
TI  - Minimal positive realizations: a survey of recent results and open problems
JO  - Kybernetika
PY  - 2003
SP  - [217]
VL  - 39
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2003__39_2_a10/
LA  - en
ID  - KYB_2003__39_2_a10
ER  - 
%0 Journal Article
%A Benvenuti, Luca
%A Farina, Lorenzo
%T Minimal positive realizations: a survey of recent results and open problems
%J Kybernetika
%D 2003
%P [217]
%V 39
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2003__39_2_a10/
%G en
%F KYB_2003__39_2_a10
Benvenuti, Luca; Farina, Lorenzo. Minimal positive realizations: a survey of recent results and open problems. Kybernetika, Tome 39 (2003) no. 2, p. [217]. http://geodesic.mathdoc.fr/item/KYB_2003__39_2_a10/