A PD-Like Protocol With a Time Delay to Average Consensus Control for Multi-Agent Systems Under an Arbitrarily Fast Switching Topology
针对线性与Lipschitz非线性多智能体系统在任意快速切换拓扑下的平均一致性问题，设计了一种带时延的比例-微分类协议，通过系统变换转化为切换时滞系统稳定性问题，并基于含三重积分项的Lyapunov-Krasovskii泛函给出充分条件。
This paper is concerned with the problem of average consensus control for multi-agent systems with linear and Lipschitz nonlinear dynamics under a switching topology. First, a proportional and derivative-like consensus algorithm for linear cases with a time delay is designed to address such a problem. By a system transformation, such a problem is converted to the stability problem of a switched delay system. The stability analysis is performed based on a proposed Lyapunov-Krasoversusii functional including a triple-integral term and sufficient conditions are obtained to guarantee the average consensus for multi-agent systems under arbitrary switching. Second, extensions to the Lipschitz nonlinear cases are further presented. Finally, numerical examples are given to illustrate the effectiveness of the results.