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In this paper, we study delayed regulated state/output synchronization fordiscrete-time homogeneous and heterogeneous networks of multi-agent systems(MAS) subject to unknown, non-uniform and arbitrarily large communicationdelays. A delay transformation is utilized to transform the original MAS to anew system without delayed states. The proposed scale-free dynamic protocolsare developed solely based on agent models and localized information exchangewith neighbors such that we do not need any information about the communicationnetworks and the number of agents.

Scale-free Design for Delayed Regulated Synchronization of Homogeneous  and Heterogeneous Discrete-time Multi-agent Systems Subject to Unknown  Non-uniform and Arbitrarily Large Communication Delays