含时变时延的多智能体的包容控制器设计

针对一类含时变通讯时延的多智能体系统，基于时滞依赖法提出了其在有向网络拓扑下的一类包容控制器设计的方法，该设计能有效地驱使多智能体系统中所有跟随者的状态渐近一致地收敛到领导者运动过程中形成的几何凸包．结合李亚普诺夫稳定性理论和线性矩阵不等式（LMI）方法，推导了多智能体系统包容控制率存在的充分条件，并将包容控制器的设计最终转化成求解线性矩阵不等式可行解的问题．结果表明，该方法对多智能体系统中的时变通讯时延具有良好的补偿效果．最后通过仿真算例验证了此方法的有效性和可行性．

Containment Controller Design for a Multi-agent System with Time-varying Delays

A design of delay-dependent containment controller under the directed network graph is proposed in this study for a class of multi-agent system with time-varying communication delays. The proposed design can effectively drive all followers' states to asymptotically converge toward the convex hull spanned by the leaders. Combining Lyapunov stability theory and linear matrix inequality (LMI) method, a sufficient condition guaranteeing containment control is derived, and the problem of containment controller design is converted to solve the problem of ensuring the feasibility of linear matrix inequality. The results show that the delay-dependent containment controller effectively helps compensate the time-varying delays. Finally, the effectiveness and feasibility of the control method are verified by using a simulation example.