The distributed stabilization problem is studied in this article for a group of heterogeneous second-order agents in the strong–weak competition network containing three kinds of relationships among agents: 1) cooperation; 2) strong competition; and 3) weak competition. The entire network satisfies the structural balance condition which can be partitioned into two subnetworks, while the strong and weak competitions are alternate actions on the agents from different subnetworks. To stabilize such heterogeneous networked systems in a distributed way, the switched system approach is developed and utilized in this article, where it is revealed that distributed stabilization can be achieved provided that the ratio on the activating periods of strong and weak competition is chosen appropriately. As an extension, a periodical switching law is taken into account to simplify the design process, where the periodical competition function is introduced correspondingly and several effective sufficient conditions are attained. Finally, the derived analytical results are demonstrated by performing numerical simulations.

中文翻译：

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强弱竞争网络中多个异构代理的分布式稳定：一种切换系统方法

本文研究了强弱竞争网络中一组异构二阶代理的分布式镇定问题，该网络包含代理之间的三种关系：1）合作；2) 竞争激烈；3) 竞争较弱。整个网络满足结构平衡条件，可以划分为两个子网络，而强弱竞争是对来自不同子网络的代理的交替动作。To stabilize such heterogeneous networked systems in a distributed way, the switched system approach is developed and utilized in this article, where it is revealed that distributed stabilization can be achieved provided that the ratio on the activating periods of strong and weak competition is chosen appropriately. 作为延伸，为了简化设计过程，考虑了周期切换律，相应地引入了周期竞争函数，得到了几个有效的充分条件。最后，通过进行数值模拟来证明导出的分析结果。