On the pinning controllability of complex networks using perturbation theory of extreme singular values. Application to synchronisation in power grids

Stéphane Chrétien (1) , Sébastien Darses (1) , Christophe Guyeux (2) , Paul Clarkson (1)

1 NPL - National Physical Laboratory [Teddington]
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

Pinning control on complex dynamical networks has emerged as a very important topic in recent trends of control theory due to the extensive study of collective coupled behaviors and their role in physics, engineering and biology. In practice, real-world networks consist of a large number of vertices and one may only be able to perform a control on a fraction of them only. Controllability of such systems has been addressed in [17], where it was reformulated as a global asymptotic stability problem. The goal of this short note is to refine the analysis proposed in [17] using recent results in singular value perturbation theory.

Mots clés: Pinned control; eigenvalue perturbation; sum of rank one matrices; singular value perturbation; control theory

Domaines: Cryptographie et sécurité [cs.CR]; Calcul parallèle, distribué et partagé [cs.DC]; Technologies Émergeantes [cs.ET]; Informatique ubiquitaire; Système multi-agents [cs.MA]; Modélisation et simulation; Génie logiciel [cs.SE]

Stéphane Chrétien, Sébastien Darses, Christophe Guyeux, Paul Clarkson. On the pinning controllability of complex networks using perturbation theory of extreme singular values. Application to synchronisation in power grids. Numerical Algebra, Control and Optimization, 2017, 7 (3), pp.289 - 299. ⟨10.3934/naco.2017019⟩. ⟨hal-02392542⟩