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.
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