Consensus of Linear Multiagent Systems With Distributed Infinite Transmission Delays: A Low Gain Approach

This paper considers the consensus problem of linear multiagent systems with distributed infinite transmission delays. A novel low gain controller is proposed and it is shown that the proposed controller can solve the consensus problem if the open loop agent dynamics have no exponentially unstable eigenvalues and the communication topology is fixed and contains a spanning tree. One of the distinctive advantages of the proposed controller is that it does not require the knowledge of transmission delays. Our proofs are established based on a stability result on infinite delays, which can be seen as an extension of the commonly used frequency domain method. Our results include those results on distributed bounded delays and constant delays as their special cases. Simulation examples are provided to illustrate the effectiveness of the proposed controller.