Semistability of Nonlinear Systems Having a Connected Set of Equilibria and Time-Delays

Abstract

In this report, we develop a semistability analysis framework for nonlinear systems with bounded timevarying 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.

Partially Informed Agents Can Form a Swarm in a Nash Equilibrium

“…Thus, B 2n+1 (τ ) is decreasing to 0 as τ → 1 if and only if n is even, which gives sign{B 2n+1 (τ )} = (−1) n , ∀τ ∈ (0.5, 1). This implies (11) by the expressions in (10).…”

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“…A classical example is the synchronization of multiple weakly coupled oscillators to a common frequency. Recently, significant results have been obtained on semistability in consensus problems for networked agents [1], [6], [10], [16]- [18]. An example of such a problem is for a group of networked autonomous vehicles to converge to a common heading, and for the network to respond to a small perturbation with only a corresponding small change to the common heading.…”