This paper addresses leader-following consensus of multi-agent systems with semi-Markovian switching topologies and time-varying delays. Unlike the classic Markovian switching topologies, the transition rates are time-varying in the semi-Markovian switching topologies, which can better model the switching of topologies due to inevitable stochastic changes. Moreover, compared with existing works on multi-agent systems with switching topologies and time delays, the delays in the paper are dependent on the switching modes. By designing the distributed mode-dependent consensus protocol and constructing Lyapunov functional, sufficient conditions in terms of LMIs are derived to ensure that leader-following consensus is asymptotically achieved in the mean square. Finally, a numerical example is provided to show the effectiveness of the main results.

中文翻译：

---

具有半马尔可夫切换拓扑和模式相关延迟的多智能体系统的 H ∞ 一致性

本文讨论了具有半马尔可夫切换拓扑和时变延迟的多智能体系统的领导者跟随共识。与经典的马尔可夫转换拓扑不同，半马尔可夫转换拓扑中的转换速率是随时间变化的，这可以更好地模拟由于不可避免的随机变化而导致的拓扑转换。此外，与具有切换拓扑和时间延迟的多代理系统的现有工作相比，本文中的延迟取决于切换模式。通过设计分布式依赖模式的共识协议并构造Lyapunov泛函，推导出LMI方面的充分条件，以确保在均方中渐近实现领导者跟随共识。最后，给出一个数值例子来说明主要结果的有效性。