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

arXiv: https://arxiv.org/abs/1906.00890 · HTML: https://mlsanity.com/paper/1906.00890/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2019.

## Built on by (most cited first, 2 of 2)

- [Optimization in Open Networks via Dual Averaging](https://mlsanity.com/paper/2105.13348/) (2021)
- [Optimization and Learning in Open Multi-Agent Systems](https://mlsanity.com/paper/2501.16847/) (2025)

## Abstract (arXiv)

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.