Stability of leaderless multi-agent systems. Extension of a result by Moreau

TL;DR

This paper extends a known result on multi-agent systems by including communication delays and relaxing convexity assumptions, showing conditions for global convergence to equilibrium.

Contribution

It generalizes Moreau's stability result to account for bounded delays and non-convex state transition regions in leaderless multi-agent systems.

Findings

Connectedness of interaction graphs ensures convergence.

Bounded communication delays do not prevent stability under certain conditions.

Relaxed convexity assumptions still guarantee global equilibrium.

Abstract

The paper presents a result which relates connectedness of the interaction graphs in a multi-agent systems with the capability for global convergence to a common equilibrium of the system. In particular we extend a previously known result by Moreau by including the possibility of arbitrary bounded time-delays in the communication channels and relaxing the convexity of the allowed regions for the state transition map of each agent.