Certified Algorithms for proving the ...
Type de document :
Communication dans un congrès avec actes
Titre :
Certified Algorithms for proving the structural stability of two dimensional systems possibly with parameters
Auteur(s) :
Bouzidi, Yacine [Auteur]
Non-Asymptotic estimation for online systems [NON-A]
Rouillier, Fabrice [Auteur]
OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs [OURAGAN]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Université Pierre et Marie Curie - Paris 6 [UPMC]
Non-Asymptotic estimation for online systems [NON-A]
Rouillier, Fabrice [Auteur]
OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs [OURAGAN]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Université Pierre et Marie Curie - Paris 6 [UPMC]
Titre de la manifestation scientifique :
MNTS 2016 - 22nd International Symposium on Mathematical Theory of Networks and Systems
Ville :
Minneapolis
Pays :
Etats-Unis d'Amérique
Date de début de la manifestation scientifique :
2016-07-11
Titre de la revue :
Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems
Date de publication :
2016-07
Mot(s)-clé(s) en anglais :
stability of multidimensional systems
computer algebra
computer algebra
Discipline(s) HAL :
Informatique [cs]/Calcul formel [cs.SC]
Résumé en anglais : [en]
In [1], a new method for testing the structural stability of multidimensional systems has been presented. The key idea of this method is to reduce the problem of testing the structural stability to that of deciding if an ...
Lire la suite >In [1], a new method for testing the structural stability of multidimensional systems has been presented. The key idea of this method is to reduce the problem of testing the structural stability to that of deciding if an algebraic set has real points. Following the same idea, we consider in this work the specific case of two-dimensional systems and focus on the practical efficiency aspect. For such systems, the problem of testing the stability is reduced to that of deciding if a bivariate algebraic system with finitely many solutions has real ones. Our first contribution is an algorithm that answers this question while achieving practical efficiency. Our second contribution concerns the stability of two dimensional systems with parameters. More precisely, given a two-dimensional system depending on a set of parameters, we present a new algorithm that computes regions of the parameter space in which the considered system is structurally stable.Lire moins >
Lire la suite >In [1], a new method for testing the structural stability of multidimensional systems has been presented. The key idea of this method is to reduce the problem of testing the structural stability to that of deciding if an algebraic set has real points. Following the same idea, we consider in this work the specific case of two-dimensional systems and focus on the practical efficiency aspect. For such systems, the problem of testing the stability is reduced to that of deciding if a bivariate algebraic system with finitely many solutions has real ones. Our first contribution is an algorithm that answers this question while achieving practical efficiency. Our second contribution concerns the stability of two dimensional systems with parameters. More precisely, given a two-dimensional system depending on a set of parameters, we present a new algorithm that computes regions of the parameter space in which the considered system is structurally stable.Lire moins >
Langue :
Anglais
Comité de lecture :
Oui
Audience :
Internationale
Vulgarisation :
Non
Collections :
Source :
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