On the duality between consensus problems and Markov processes, with application to delay systems

TL;DR

This paper explores the duality between consensus problems in multi-agent systems and Markov processes, providing a unified framework to analyze and incorporate delays, and deriving conditions for consensus and its value.

Contribution

It introduces a novel unified framework linking consensus and Markov processes, allowing analysis of delays in multi-agent systems.

Findings

Derived conditions for reaching consensus with delays

Calculated consensus values under different delay scenarios

Unified treatment of information propagation and processing delays

Abstract

We consider consensus of multi-agent systems as a dual problem to Markov processes. Based on an exchange of relevant notions and results between the two fields, we present a uniform framework which admits the introduction and treatment of time delays in a common setting. We study both information propagation and information processing delays, and for each case derive conditions for reaching consensus and calculate the consensus value.