no. 5-6
Analytic Geometry/Automation (theoretical)
A toric Positivstellensatz with applications to delay systems

Présenté par : Philippe G. Ciarlet

Niculescu, Silviu-Iulian1 ; Putinar, Mihai2
1 Laboratoire des signaux et systèmes (UMR CNRS 8506), 3, rue Joliot-Curie, 91192 Gif-sur-Yvette, France
2 Mathematics Department, University of California, Santa Barbara, CA 93106, USA
Comptes Rendus. Mathématique, Tome 349 (2011) no. 5-6, pp. 327-329.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.11.018
Niculescu, Silviu-Iulian 1 ; Putinar, Mihai 2

1 Laboratoire des signaux et systèmes (UMR CNRS 8506), 3, rue Joliot-Curie, 91192 Gif-sur-Yvette, France
2 Mathematics Department, University of California, Santa Barbara, CA 93106, USA 
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Niculescu, Silviu-Iulian; Putinar, Mihai. A toric Positivstellensatz with applications to delay systems. Comptes Rendus. Mathématique, Tome 349 (2011) no. 5-6, pp. 327-329. doi : 10.1016/j.crma.2010.11.018. http://www.numdam.org/articles/10.1016/j.crma.2010.11.018/

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☆ Partially supported by CNRS, France and the National Science Foundation, USA.