Consensus under Persistence Excitation

TL;DR

This paper proves that a first-order cooperative multi-agent system reaches consensus under a Persistence Excitation condition, which guarantees sufficient interaction over time through an integral lower bound.

Contribution

It introduces the Persistence Excitation condition as a sufficient criterion for consensus in cooperative systems, providing a new theoretical insight.

Findings

Consensus is achieved when the Persistence Excitation condition holds.

The interaction function must satisfy an integral lower bound.

The condition ensures minimal interaction over time.

Abstract

We prove that a first-order cooperative system of interacting agents converges to consensus if the so-called Persistence Excitation condition holds. This condition requires that the interaction function between any pair of agents satisfies an integral lower bound. The interpretation is that the interaction needs to ensure a minimal amount of service.