Multi-Agent Bipartite Tracking Control Over General Cooperative-Hostile Networks

This brief investigates the problem of bipartite tracking control for general linear multi-agent systems with cooperation and hostility. Compared with the existing studies over structurally balanced networks where hostile relations can only exist between two agent subgroups, the main highlight of this brief is to extend the bipartite tracking behavior to a more general cooperative-hostile network, in which hostile relations can exist within and between agent subgroups at the same time. Based on products of super-stochastic matrices, a sufficient criterion related to the network structure, such as network connectivity and positive and negative edge weights, is established. Meanwhile, it is also shown theoretically that each subsystem can be allowed to be strictly unstable, and the upper bound of unstable eigenvalue modules of the system matrix is given. Finally, a simulation example is provided to demonstrate the effectiveness of the theoretical result.