Abstract In this paper, we introduce linear multi-agent systems (MASs) composed of a conformable derivative. The protocol of each agent is designed by using its local information. Two sufficient and necessary conditions are derived for the consensus of the systems respectively under the topologies of undirected and directed networks based on algebraic graph theory and matrix theory. Meanwhile, the relationship between the agreement values and topology structures is discussed. Finally, we demonstrate the theoretical results and the advantage of the systems compared with traditional integer order systems by several numerical simulations.

中文翻译：

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涉及一致导数的线性多智能体系统的共识问题

摘要 在本文中，我们介绍了由一致导数组成的线性多智能体系统 (MAS)。每个代理的协议是利用其本地信息设计的。基于代数图论和矩阵论的无向和有向网络拓扑分别推导出系统一致性的两个充分必要条件。同时，讨论了协议值与拓扑结构之间的关系。最后，我们通过几个数值模拟证明了该系统与传统整数阶系统相比的理论结果和优势。