Stability of multiagent systems with time-dependent communication links

TLDR

The model applies to synchronization, swarming, and distributed decision making. We study a simple model of agents interacting via time‑dependent communication links and present necessary and sufficient conditions for convergence to a common value, extending recent results. Agents update their states based on current neighbor information, and stability is analyzed using graph‑theoretic, system‑theoretic, and convexity tools within a set‑valued Lyapunov framework. More communication does not always speed convergence and can even prevent convergence in these models.

Abstract

We study a simple but compelling model of network of agents interacting via time-dependent communication links. The model finds application in a variety of fields including synchronization, swarming and distributed decision making. In the model, each agent updates his current state based upon the current information received from neighboring agents. Necessary and/or sufficient conditions for the convergence of the individual agents' states to a common value are presented, thereby extending recent results reported in the literature. The stability analysis is based upon a blend of graph-theoretic and system-theoretic tools with the notion of convexity playing a central role. The analysis is integrated within a formal framework of set-valued Lyapunov theory, which may be of independent interest. Among others, it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence, even for the simple models discussed in the present paper.