Abstract We consider consensus in this paper for hybrid multi-agent systems (HMASs) consisting of continuous-time dynamic agents and discrete-time dynamic agents via designing pulse-modulated protocols. By assuming all the agents communicate with its neighbors only at some sampling instants, and the input of each continuous-time agent is determined by a pulse function, the consensus for first-order HMASs and second-order HMASs are addressed, respectively. According to the model transformation, stochastic matrix theory and the mathematical analysis technique, some sufficient criteria for consensus of these two types of HMASs are derived where it shows that the consensus in the considered HMASs can be achieved when the network structure, pulse function and sampling period respectively satisfy some suitable conditions. And, an algorithm is presented to evaluate the maximum allowable sampling period for achieving consensus. Finally, three numerical simulation examples are performed to validate the main theoretical results.

中文翻译：

---

具有脉冲调制协议的混合多代理系统的共识

摘要 我们通过设计脉冲调制协议，在本文中考虑了由连续时间动态代理和离散时间动态代理组成的混合多代理系统（HMAS）的共识。通过假设所有代理仅在某些采样时刻与其邻居通信，并且每个连续时间代理的输入由脉冲函数确定，分别解决了一阶 HMAS 和二阶 HMAS 的共识。根据模型转换、随机矩阵理论和数学分析技术，推导出了这两种类型的 HMAS 一致性的一些充分标准，表明当网络结构、脉冲函数和采样时，所考虑的 HMAS 中的一致性可以实现期间分别满足一些合适的条件。和，提出了一种算法来评估实现共识的最大允许采样周期。最后，通过三个数值模拟实例验证了主要的理论结果。