Linear Consensus Algorithms Based on Balanced Asymmetric Chains

TL;DR

This paper analyzes multi-agent consensus algorithms using balanced asymmetric chains, establishing conditions for finite accumulation points and linking consensus behavior to the property of absolute infinite flow.

Contribution

It introduces a novel analysis framework for consensus algorithms based on balanced asymmetric chains and relates convergence properties to the absolute infinite flow condition.

Findings

Finite set of accumulation points for agent states.

Consensus or multiple consensuses depend on absolute infinite flow.

Results apply to well-known consensus models.

Abstract

Multi agent consensus algorithms with update steps based on so-called balanced asymmetric chains, are analyzed. For such algorithms it is shown that (i) the set of accumulation points of states is finite, (ii) the asymptotic unconditional occurrence of single consensus or multiple consensuses is directly related to the property of absolute infinite flow for the underlying update chain. The results are applied to well known consensus models.