A Decomposition Approach to Multi-Agent Systems with Bernoulli Packet Loss

TL;DR

This paper introduces a scalable decomposition method for analyzing large multi-agent systems affected by Bernoulli packet loss, providing stability and performance conditions expressed as linear matrix inequalities.

Contribution

It extends the decomposable systems framework to handle Bernoulli packet loss in multi-agent systems with conditions that scale linearly with network size.

Findings

Conditions for mean-square stability derived as LMIs

Performance analysis via $H_2$-norm bounds

Numerical example on consensus problem demonstrates effectiveness

Abstract

In this paper, we extend the decomposable systems framework to multi-agent systems with Bernoulli distributed packet loss with uniform probability. The proposed sufficient analysis conditions for mean-square stability and $H_2$-performance -- which are expressed in the form of linear matrix inequalities -- scale linearly with increased network size and thus allow to analyse even very large-scale multi-agent systems. A numerical example demonstrates the potential of the approach by application to a first-order consensus problem.