This document shows that the proof of Theorem 3.3 in the work of Liu et al (Int J Robust Nonlinear Control. 2015. 10.1002/rnc.3108) is incorrect and, thus, the theorem is not proved. Since the results of the paper are strongly based on this theorem, the problem has to be addressed. If a natural correction is introduced, the problem still holds. Therefore, a new linear matrix inequality is proposed here to show its equivalence with the stochastic stability of a Markov jump linear singular system under a similar assumption as that in the work of Liu et al.