La structure des polynômes positifs sur un tore est déduite à lʼaide de deux théorèmes récents de type Positivstellensatz. Comme application, on propose des conditions simples pour vérifier lʼhyperbolicité/stabilité dʼun système linéaire générique dʼéquations différentielles de type retardé.
The structure of positive polynomials on a torus is derived from recent results of real algebraic geometry. As an application, we propose some simple conditions for testing the hyperbolicity/stability of a generic class of linear systems of retarded type.
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@article{CRMATH_2011__349_5-6_327_0,
author = {Silviu-Iulian Niculescu and Mihai Putinar},
title = {A toric {Positivstellensatz} with applications to delay systems},
journal = {Comptes Rendus. Math\'ematique},
pages = {327--329},
publisher = {Elsevier},
volume = {349},
number = {5-6},
year = {2011},
doi = {10.1016/j.crma.2010.11.018},
language = {en},
}
Silviu-Iulian Niculescu; Mihai Putinar. A toric Positivstellensatz with applications to delay systems. Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 327-329. doi : 10.1016/j.crma.2010.11.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.018/
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☆ Partially supported by CNRS, France and the National Science Foundation, USA.
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