  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.
