Research on Leader-Following Consensus of Multi-Agent Systems under Switching Topologies

本文研究了切换拓扑下一类线性离散网络的领导跟随一致性问题，考虑随着时间的变化，多智能体间的通信可能会在某一段时间连通性变差，即部分通信拓扑的子拓扑不包含有向生成树。针对这种情况，首先，设计基于状态反馈的控制协议，并通过图矩阵不等式与改进的黎卡提方程构造李雅普诺夫函数。其次，基于平均驻留时间的方法，通过分类讨论，得到了有向切换网络实现一致性的充分条件。最后，通过一个仿真实例验证了结果的有效性。This paper investigates the leader-following consensus problem for a class of linear discrete networks under switching topologies. It considers that the communication among multi-agents may deteriorate over time, meaning that some sub-topologies of the communication topology do not contain a directed spanning tree. To address this issue, a state feedback-based control protocol is first designed, and a Lyapunov function is constructed using graph matrix inequalities and an improved Riccati equation. Subsequently, by employing the average dwell time method and through categorical discussion, sufficient conditions for achieving consensus in directed switching networks are derived. Finally, the effectiveness of the results is validated through a simulation example.