Distributed Stabilization of Multiple Heterogeneous Agents in the Strong-Weak Competition Network: A Switched System...

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.