It is known that time delays play an important role in the dynamics of artificial neural networks, leading eventually to self-sustained oscillations and instability. This paper provides a new criterion for asymptotic stability of a nonlinear delay differential system. If
is the delay parameter, it is proved that the origin is globally exponentially stable for any
if a suitable linear matrix inequality (LMI) is verified. Such LMI can be checked numerically and the upper bound
can be computed explicitly by solving a quasi-convex matrix optimization problem. Two illustrative examples show the practical applicability of the criterion.