Rotating consensus for double-integrator multi-agent systems with communication delay

In this paper, the rotating consensus problem for the multi-agent systems of double-integrator dynamic is mainly considered with and without communication delay. A fully distributed control strategy is given on the more general complex plane. For the case without communication delay, we design a distributed control protocol with the help of local relative information and obtain the sufficient and necessary condition with the lower bounded control parameter for the directed communication topology. Furthermore, with taking communication delay into consideration, the sufficient and necessary condition with the upper bounded communication delay is obtained with the help of frequency domain analysis method. Compared with some existing results, the communication topology considered is a more general directed graph. Finally, some simulation examples are presented to clarify the correctness of our results.