Single-Delay and Multiple-Delay Proportional-Retarded (PR) Protocols for Fast Consensus in a Large-Scale Network

A distributed proportional-retarded (PR) protocol is proposed for a class of large-scale consensus system with single-integrator agent dynamics. The protocol, a part of which utilizes intentional delays, enables fast consensus mainly by placing system's dominant poles and separating the rest of the spectrum from these poles as desired. The PR protocol rests upon spectral analysis and salient features of Lambert W functions, and ultimately helps compose the graph Laplacian of the network as a complete graph.