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.

中文翻译：

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具有通信延迟的二阶有符号网络的分布式控制器设计与分析

本文专注于处理不仅受合作而且受对抗互动影响的二阶有符号网络的分布式控制问题。提出了一种基于最近邻规则的分布式控制协议，该协议为二阶有符号网络的共识开发了充分条件，该网络的通信拓扑由强连通有符号有向图描述。此外，还设计了另一种存在通信延迟的分布式控制协议，可以同时确定延迟的时间余量。结果表明，在延迟裕度条件下，即使考虑具有通信延迟的二阶有符号网络，也可以得出充分必要的共识结果。