# Delayed state synchronization of continuous-time multi-agent systems in the presence of unknown communication delays (including complete proofs)

## TL;DR

This paper introduces a delay-free transformation method for continuous-time multi-agent systems to achieve synchronization despite unknown communication delays, providing protocols for both homogeneous and heterogeneous systems.

## Contribution

It develops a novel delay-free transformation and protocols for delayed synchronization in multi-agent systems with unknown nonuniform delays, including proofs and output synchronization strategies.

## Key findings

- Successfully transforms delayed MAS to delay-free systems
- Designs static and dynamic protocols for synchronization
- Achieves output synchronization for heterogeneous MAS

## Abstract

This paper studies delayed synchronization of continuous-time multi-agent systems (MAS) in the presence of unknown nonuniform communication delays. A delay-free transformation is developed based on a communication network which is a directed spanning tree, which can transform the original MAS to a new one without delays. By using this transformation, we design a static protocol for full-state coupling and a dynamic protocol for delayed state synchronization for homogeneous MAS via full- and partial-state coupling. Meanwhile, the delayed output synchronization is also studied for heterogeneous MAS, which is achieved by using a low-gain and output regulation based dynamic protocol design via the delay-free transformation.