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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.
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https://hal.inria.fr/hal-01263384
Contributor : Marianne Akian <>
Submitted on : Wednesday, January 27, 2016 - 4:53:41 PM
Last modification on : Friday, April 30, 2021 - 9:57:58 AM

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  • HAL Id : hal-01263384, version 1

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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. SIAM Conference on Control and its Applications (SIAM CT’15), Jul 2015, Paris, France. ⟨hal-01263384⟩

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