Distributed L ₂ − L∞ consensus of multi-agent systems under asynchronous switching topologies

Abstract

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 L2−L∞ 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 L2−L∞ 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.