  In the analysis of consensus problems for multi-agent systems affected by
time delays, the delay margin for a given protocol is heavily dependent on the
communication topology being used. This document aims to answer the question of
what is the largest delay value under which convergence to consensus is still
possible even if the communication topology is not known. To answer this
question we revisit the concept of most exigent eigenvalue, applying it to two
different consensus protocols for agents driven by second order dynamics. We
show how the delay margin depends on the structure of the consensus protocol
and the communication topology, and arrive to a boundary that guarantees
consensus for any connected communication topology. The switching topologies
case is also studied and It is shown that for one protocol the stability of the
individual topologies is sufficient to guarantee consensus in the switching
case, whereas for the other one it is not.
