  In this report, we develop a semistability analysis framework for nonlinear
systems with bounded time-varying delays with applications to stability
analysis of multiagent dynamic networks with consensus protocols in the
presence of unknown heterogeneous time-varying delays along the communication
links. We show that for such a nonlinear system having nonisolated equilibria,
if the system asymptotically converges to a constant time-delay system and this
new system is semistable, then the original time-varying delay system is
semistable. In proving our results, we extend the limiting differential
equation approach to time-varying delay systems and also develop some new
convergence results for functional differential equations.
