# Connectivity-Preserving Coordination Control of Multi-Agent Systems with Time-Varying Delays

## TL;DR

This paper introduces a distributed control method for multi-agent systems that ensures connectivity preservation and synchronization despite the challenges posed by time-varying communication delays.

## Contribution

It proposes a novel control strategy combining potential energy-based control with damping via a dynamic filter, extending to Euler-Lagrange systems.

## Key findings

- Ensures all agents stay within communication range.
- Achieves asymptotic stability of the multi-agent system.
- Validated through Lyapunov analysis and simulations.

## Abstract

This paper presents a distributed position synchronization strategy that also preserves the initial communication links for single-integrator multi-agent systems with time-varying delays. The strategy employs a coordinating proportional control derived from a specific type of potential energy, augmented with damping injected through a dynamic filter. The injected damping maintains all agents within the communication distances of their neighbours, and asymptotically stabilizes the multi-agent system, in the presence of time delays. Regarding the closed-loop single-integrator multi-agent system as a double-integrator system suggests an extension of the proposed strategy to connectivity-preserving coordination of Euler-Lagrange networks with time-varying delays. Lyapunov stability analysis and simulation results validate the two designs.