A Note on the Consensus Finding Problem in Communication Networks with Switching Topologies

TL;DR

This paper analyzes how agents in communication networks with changing directed topologies can reach consensus, establishing conditions for asymptotic convergence based on graph connectivity and system dynamics.

Contribution

It provides new sufficient conditions for consensus in directed switching networks with unbalanced communication matrices, emphasizing the emergent nature of consensus.

Findings

Consensus is achieved asymptotically under strong connectivity.

Consensus emerges from system dynamics, not initial conditions.

Conditions apply to directed networks with unbalanced matrices.

Abstract

In this note, we discuss the problem of consensus finding in communication networks of agents with dynamically switching topologies. In particular, we consider the case of directed networks with unbalanced matrices of communication rates. We formulate sufficient conditions for consensus finding in terms of strong connectivity of the underlying directed graphs and prove that, given these conditions, consensus is found asymptotically. Moreover, we show that this consensus is an emergent property of the system, being encoded in its dynamics and not just an invariant of its initial configuration.