  In this brief note, we establish a novel criterion for robustness of global
asymptotic stability of zero solution of LTV system $\dot x=A(t)x$ in the
presence of possibly unbounded perturbations (external disturbances). To prove
the result, logarithmic norm will be used under which the stability becomes a
topological notion depending on the chosen vector norm in the state-space
$\mathbb{R}^n.$
