Open AccessAsymmetric bipartite consensus over directed networks with antagonistic interactions
Author(s) -
Guo Xing,
Liang Jinling,
Lu Jianquan
Publication year - 2018
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2018.5060
Subject(s) - digraph , bipartite graph , spanning tree , eigenvalues and eigenvectors , strongly connected component , mathematics , signed graph , laplacian matrix , combinatorics , directed graph , consensus , class (philosophy) , discrete mathematics , laplace operator , topology (electrical circuits) , multi agent system , computer science , graph , artificial intelligence , mathematical analysis , physics , quantum mechanics
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.