Abstract: In this paper, the group consensus problem for mixed-order multi-agent systems is studied, where the multi-agent system is composed of discrete-time first-and second-order agents under fixed and switching topologies with communication delays. Firstly, group consensus protocols are proposed for two kinds of agents. Then model transformation is introduced to transform the closed-loop system into an equivalent system. Under certain assumptions, algebraic graph theory and matrix theory are utilized to derive conditions under which multi-agent systems with fixed and switching topologies will reach group consensus asymptotically, respectively. Finally, the effectiveness of the results obtained in the paper is validated by numerical simulations.

Key words: discrete-time mixed-order multi-agent system, communication delay, group consensus

摘要： 针对由离散时间一阶和二阶智能体组成的混合阶多智能体系统，研究其在固定和切换拓扑结构下受通信时滞影响时的组一致性问题。分别为两类智能体提出组一致性协议，引入模型变换，将闭环系统转化为等价系统。在一定假设条件下，以代数图论、矩阵理论为主要研究工具，分别在固定和切换拓扑结构下给出了混合阶多智能体系统实现渐近组一致性的条件。采用数值仿真对所得结果的有效性进行了验证。

关键词: 离散时间混合阶多智能体系统, 通信时滞, 组一致性