Distributed Controller Design and Analysis of Second-Order Signed Networks With Communication Delays.

This article concentrates on dealing with distributed control problems for second-order signed networks subject to not only cooperative but also antagonistic interactions. A distributed control protocol is proposed based on the nearest neighbor rules, with which necessary and sufficient conditions are developed for consensus of second-order signed networks whose communication topologies are described by strongly connected signed digraphs. Besides, another distributed control protocol in the presence of a communication delay is designed, for which a time margin of the delay can be determined simultaneously. It is shown that under the delay margin condition, necessary and sufficient consensus results can be derived even though second-order signed networks with a communication delay are considered. Simulation examples are included to illustrate the validity of our established consensus results of second-order signed networks.