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

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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Dates and versions

hal-01263384 , version 1 (27-01-2016)

Identifiers

  • HAL Id : hal-01263384 , version 1

Cite

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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