  We study the delay margin problem in the context of recent works by T. Qi, J.
Zhu, and J. Chen, where a sufficient condition for the maximal delay margin is
formulated in terms of an interpolation problem obtained after introducing a
rational approximation. Instead we omit the approximation step and solve the
same problem directly using techniques from function theory and analytic
interpolation. Furthermore, we introduce a constant shift in the domain of the
interpolation problem. In this way we are able to improve on their lower bound
for the maximum delay margin.
