Further comments on "Vector norms as Lyapunov functions for linear systems"

This paper deals with the conditions for a vector norm to be a Lyapunov function for a linear time-invariant system. An error in the proof of the related theorem given in Hmamed (1994) is pointed out, and a counterexample proving that this theorem is generally false is provided. It is demonstrated that the considered problem is related to the one of extending a linear operator without increasing its norm.