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

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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.