In this paper, the leader-following consensus is investigated for general linear multi-agent systems under external disturbances. The communication topologies are time-varying and switched from a finite set. To model these topologies, a signal with average dwell time switching is introduced. The overall closed-loop system is described as a switched control system. The notion of weighted $L_2-L_{\mathrm{\infty }}$ performance is then introduced and analysed. Based on the local information obtained from the neighbours, a topology-dependent controller is designed. The switchings between the communication topologies and the controllers are asynchronous. Conditions are developed for the existence of a control protocol to produce the leader-following consensus with a certain level of weighted $L_2-L_{\mathrm{\infty }}$ performance. The design algorithm is then formulated as a set of linear matrix inequalities (LMIs). A numerical example is then given to show the effectiveness of the proposed consensus algorithm.

在本文中，研究了外部干扰下一般线性多智能体系统的领导者跟随共识。通信拓扑是时变的，并且是从有限集切换的。为了对这些拓扑进行建模，引入了具有平均停留时间切换的信号。整个闭环系统被描述为一个开关控制系统。加权的概念${\mathrm{大号}}_2-{\mathrm{大号}}_{\mathrm{\infty }}$然后介绍和分析性能。基于从邻居获得的本地信息，设计了一个拓扑相关的控制器。通信拓扑和控制器之间的切换是异步的。为存在控制协议制定条件，以产生具有一定加权水平的领导者跟随共识${\mathrm{大号}}_2-{\mathrm{大号}}_{\mathrm{\infty }}$表现。然后将设计算法表述为一组线性矩阵不等式 (LMI)。然后给出一个数值例子来展示所提出的共识算法的有效性。