Server-Client Consensus of Multi-Agent Systems with Time Delay

Inspired by the server-centric coordination strategies of federated learning, we propose a server-client consensus of multi-agent systems with time delay. The system consists of one server and multiple clients. The server is connected to only a subset of the clients, while connections among the remaining clients ensure that the server is globally reachable. The server processes and retransmits data from its connected clients. In a server-client system, the integration of server inevitably introduces significant and non-negligible communication delays between the server and clients, necessitating explicit consideration of these delays. Based on Lyapunov-Razumikhin method, sufficient conditions of achieving consensus with time delay are obtained. Finally, the simulation examples illustrate the obtained results.