Controllability of complex networks using perturbation theory of extreme singular values

TL;DR

This paper refines the analysis of controlling large complex networks by applying recent singular value perturbation theory, enhancing understanding of how partial control influences network stability.

Contribution

It introduces a novel approach using perturbation theory of extreme singular values to analyze network controllability, improving upon previous stability-based methods.

Findings

Enhanced analysis of network controllability using singular value perturbation

Provides bounds on control effectiveness with partial network control

Improves theoretical understanding of stability in controlled complex networks

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