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

Semistability of Nonlinear Systems Having a Continuum of Equilibria and Time-Varying Delays