Consensus on Time-Delay Intervals in Networks of High-Order Integrator Agents∗

This paper brings out a structured methodology for identifying time-delay intervals where consensus in directed networks of multiple agents with high-order integrator dynamics is achieved. It is built upon the stability analysis of a transformed consensus problem. Furthermore, particular results are derived for networks of agents with first-and second-order integrator dynamics, which can be consensusable only on the first time-delay interval, showing the value of the upper bound of this interval. The paper is closed by showing an interesting example of a network of third-order integrator agents that is not consensusable when free of delay, but it is consensusable when the control input is delayed in a proper interval.