Asymmetric bipartite consensus over directed networks with antagonistic interactions

This study deals with the bipartite consensus problem for multi‐agent systems associated with signed digraphs. For structurally balanced signed digraphs, by constructing a new class of general Laplacian matrices, it is found that all agents will converge to two values with different modulus if the signed digraph is strongly connected. Interestingly, these two values completely depend on the left eigenvector of the general Laplacian matrix corresponding to the zero eigenvalue and the initial states of all agents. Furthermore, it is shown that all agents can reach interval asymmetric bipartite consensus if the associated signed digraph contains a spanning tree. In particular, some useful results are also presented for specific signed digraphs with spanning trees. Finally, two numerical examples are provided to demonstrate the effectiveness of the main results.