Interval consensus problem of multi-agent systems with time-delay

Interval consensus problem of multi-agent systems is a new consensus problem in which the multi-agent system given by the proposed protocol can globally asymptotically converge to a specified point on the closed and bounded interval. In this paper, we discuss interval consensus problem of multi-agent systems with two types of time-delays, i.e., communication delay and input delay. Our work shows that the communication delay does not affect the consensus while the input delay does. For communication delay, the system given by the proposed protocol can reach globally asymptotically interval consensus with any time delay. As for bounded input delay, the system given by the proposed protocol can reach globally asymptotically interval consensus and then the system can also achieve a generalized interval average-consensus if the directed graph is balanced. Simulations are provided that demonstrate the effectiveness of our theoretical results.