# Stability of Open Multi-Agent Systems and Applications to Dynamic Consensus

## TL;DR

This paper introduces a new theoretical framework to analyze the stability of open multi-agent systems where agents can join or leave at any time, focusing on scalar agents and dynamic consensus algorithms.

## Contribution

It proposes a novel stability notion for OMAS and derives conditions ensuring stability despite agent arrivals and departures, with an application to dynamic consensus.

## Key findings

- Derived sufficient stability conditions for OMAS.
- Re-formulated dynamic consensus for open systems.
- Characterized stability of the open proportional dynamic consensus.

## Abstract

In this technical note we consider a class of multi-agent network systems that we refer to as Open Multi-Agent Systems (OMAS): in these multi-agent systems, an indefinite number of agents may join or leave the network at any time. Focusing on discrete-time evolutions of scalar agents, we provide a novel theoretical framework to study the dynamical properties of OMAS: specifically, we propose a suitable notion of stability and derive sufficient conditions to ensure stability in this sense. These sufficient conditions regard the arrival/departure of an agent as a disturbance: consistently, they require the effect of arrivals/departures to be bounded (in a precise sense) and the OMAS to be contractive in the absence of arrivals/departures. In order to provide an example of application for this theory, we re-formulate the well-known Proportional Dynamic Consensus for Open Multi-Agent Systems and we characterize the stability properties of the resulting Open Proportional Dynamic Consensus algorithm.