Input delay margin for consensusability of multi-agent systems

In this paper, we are concerned with the consensus of multi-agent systems with input delay. Among all standard static protocols that achieve the consensus for the multi-agent system under no input delay, we aim to find the maximum input delay such that the system remains consensusable under the same protocols. In the case of continuous-time systems, in view of the continuity of stability with respect to the time delay, the maximum delay margin for consensusability is given for scalar systems and vector systems with a single unstable open-loop pole. For scalar discrete-time systems, we show that the maximum delay margin for consensusability is strictly greater than zero if and only if the open-loop pole of the system is located in a specified interval.