Consensus on the average in arbitrary directed network topologies with time-delays

TL;DR

This paper analyzes the stability of a consensus on the average algorithm in directed networks with time-delays, showing it remains stable under small delays across various topologies.

Contribution

It introduces a storage variable to maintain average information and proves stability of the algorithm for any strongly connected directed graph with small delays.

Findings

Algorithm is stable for small delays in any directed network

Simulation results estimate maximum tolerable delays

The method applies to unbalanced directed topologies

Abstract

In this preliminary paper we study the stability property of a consensus on the average algorithm in arbitrary directed graphs with respect to communication/sensing time-delays. The proposed algorithm adds a storage variable to the agents' states so that the information about the average of the states is preserved despite the algorithm iterations are performed in an arbitrary strongly connected directed graph. We prove that for any network topology and choice of design parameters the consensus on the average algorithm is stable for sufficiently small delays. We provide simulations and numerical results to estimate the maximum delay allowed by an arbitrary unbalanced directed network topology.