Distributed multi-agent coordination: A comparison lemma based approach

In this paper, we focus on the study of distributed multi-agent coordination, including leaderless consensus and consensus tracking, by using a comparison lemma based approach. First, we investigate and present general comparison lemmas for vector differential equations that are represented in terms of upper right-hand derivatives. By using the general comparison lemmas, the stability of linear/nonlinear closed-loop systems can be guaranteed given that some properly designed linear/nonlinear systems are stable. This provides an important tool in the stability analysis of linear/nonlinear closed-loop systems by making use of known results in linear/nonlinear systems. Second, we apply the general comparison lemmas in the stability analysis of two distributed multi-agent coordination problems, namely, leaderless consensus and consensus tracking. We propose general nonlinear distributed algorithms and derive mild conditions to guarantee convergence by using the general comparison lemmas.