Eigenvectors of Non-Linear Maps on the Cone of Positive Semidefinite Matrices Application to Stability Analysis

Nikolas Stott; Xavier Allamigeon; Stéphane Gaubert; Eric Goubault; Sylvie Putot

Eigenvectors of Non-Linear Maps on the Cone of Positive Semidefinite Matrices Application to Stability Analysis

Nikolas Stott ^{1, 2} Xavier Allamigeon ^{1, 2} Stéphane Gaubert ^{1, 2} Eric Goubault ³ Sylvie Putot ³

1 MAXPLUS - Max-plus algebras and mathematics of decision

CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France

2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

3 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

Abstract : We show that the problem of synthesis of a common Lyapunov function for some classes of switched linear systems can be approached by solving an eigenproblem involving a nonlinear map on the cone of positive semidefinite matrices. This map involves the selection of a maximal lower bound of a family of matrices in this cone. We present some variants of the power algorithm, allowing one to solve the nonlinear eigenproblem in a scalable way.

Type de document :

Communication dans un congrès

SIAM Conference on Control and its Applications (SIAM CT’15), Jul 2015, Paris, France. 〈http://www.siam.org/meetings/ct15/index.php〉

Domaine :

Mathématiques [math] / Optimisation et contrôle [math.OC]

Liste complète des métadonnées

https://hal.inria.fr/hal-01263384
Contributeur : Marianne Akian <>
Soumis le : mercredi 27 janvier 2016 - 16:53:41
Dernière modification le : mercredi 14 novembre 2018 - 15:20:12

Eigenvectors of Non-Linear Maps on the Cone of Positive Semidefinite Matrices Application to Stability Analysis

Identifiants

Collections

Citation

Exporter

Métriques

332

Contact

Eigenvectors of Non-Linear Maps on the Cone of Positive Semidefinite Matrices Application to Stability Analysis

Identifiants

Collections

Citation

Exporter

Partager

Métriques

332

Contact