Consensus of Linear Multi-Agent Systems with Distributed Infinite Transmission Delays : A Low Gain Method

This paper considers the consensus problem of linear multi-agent systems with distributed infinite transmission delays. A novel low gain feedback control approach is proposed and it is shown that our proposed approach can solve the consensus problem if the open loop dynamics do not have any exponentially unstable component. It is also shown that in a special case when the open loop dynamics have all their eigenvalues at the origin, the structure of proposed controller could be much simpler. Our work is the first attempt on the consensus problem of general linear multi-agent systems with distributed infinite delays. Another distinctive advantage of our work is that the knowledge of delays is not required to be known. Moreover, the bounded distributed delays and the constant delays can be included as our special cases. Two simulation examples are proposed to illustrate the effectiveness of our results.