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

TL;DR

This paper introduces a semistability analysis framework for nonlinear systems with bounded, time-varying delays, focusing on multiagent networks with unknown delays, extending existing methods to more complex delay scenarios.

Contribution

It develops a novel semistability analysis approach for nonlinear systems with time-varying delays, including applications to multiagent consensus protocols with unknown delays.

Findings

Established conditions for semistability of systems with time-varying delays.

Extended the limiting differential equation approach to delay systems.

Provided new convergence results for functional differential equations.

Abstract

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.