On leaderless consensus of incommensurate order multi-agent systems

This article concerns the leaderless consensus problem of incommensurate-order multi-agent systems. First, a detailed analysis of the consensus between two agents with incommensurate order is shown. From this, one can conclude that consensus behavior exists in such cases. Furthermore, the initial value of the agent with a lower order will decide the consensus state. Second, a general incommensurate order multi-agent system is investigated under the directed ring topology, and the results imply that the consensus behavior also exists in such a topology. At the same time, the initial values of the agent with minimum order will determine the consensus state. Finally, some numerical examples are given to show the effectiveness of the aforementioned theoretical results. In addition, several attempts are given just by simulations when the topology is undirected and connected, and some discussions are conducted in the end.