Bipartite tracking consensus for general linear multi-agent systems with asynchronous communications over signed networks

In this paper, the bipartite tracking consensus problem of general linear multi-agent systems over signed networks is investigated, in which an asynchronous communication manner is adopted. The asynchronous setting refers to that the clocks of each agent, at which the agent's dynamics is updated, are independent of others. Relying on some related properties of the sub-stochastic matrix, the dynamics of the agents under the proposed asynchronous consensus protocol is rigorously checked. It is shown that the bipartite tracking consensus is implemented if the signed digraph contains a spanning tree. A simulation example is provided to verify our theoretical findings.