Controllability of complex networks using perturbation theory of extreme singular values

2016/01/22 by Stéphane Chrétien, Chretien, Stephane, Sébastien Darses +1
Computer Science · Mathematics · #FOS: Mathematics #Graph theory and applications #Neural Networks Stability and Synchronization #Optimization and Control (math.OC) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1601.06042

openalex publication_date 2016/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 consists 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 \citePorfiriDiBernardo:Automatica08, where it was reformulated as a global asymptotic stability problem. The goal of this short note is to refine the analysis proposed in \citePorfiriDiBernardo:Automatica08 using recent results in singular value perturbation theory.

Citations

• Perturbation bounds on the extremal singular values of a matrix after appending a column

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