A method for matrix and system stabilization (Nicola Guglielmi, L'Aquila)

05.07.2017 10:15

We consider the problem of stabilizing a matrix by a correction of minimal norm: Given a square matrix that has some eigenvalues with positive real part, find the nearest matrix having no eigenvalue with positive real part. It can be further required that the correction has a prescribed structure, e.g., to be real, to have a prescribed sparsity pattern, or to have a given maximal rank.

We propose and study a novel approach to this non-convex and non-smooth optimization problem, based on the solution of low-rank matrix differential equations. This enables us to compute locally optimal solutions in a fast way, also for higher-dimensional problems.

Illustrative numerical experiments provide evidence of the efficiency of the method. It is further shown that the approach applies equally to the related problems of closed-loop stabilization of control systems and to the stabilization of gyroscopic systems.

This is a joint work with Christian Lubich.


salle 623, Séminaire d'analyse numérique

Organisé par

Section de mathématiques


Nicola Guglielmi, University of L'Aquila

entrée libre


Catégorie: Séminaire

Mots clés: analyse numérique