Stability of Open Multiagent Systems and Applications to Dynamic Consensus

In this article, we consider a class of multiagent network systems that we refer to as open multiagent systems (OMASs): in these multiagent 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 OMASs. Specifically, we propose a suitable notion of stability and derive sufficient conditions for it. Our analysis regards the arrival/departure of agents as a disturbance; consistently, our stability conditions require the effect of arrivals/departures to be bounded (in a precise sense) and the OMASs to be contractive in the absence of arrivals/departures. In order to provide an example of application for this theory, we reformulate the well-known proportional dynamic consensus for OMASs, and we study the stability properties of the resulting open proportional dynamic consensus algorithm.