Static Bipartite Consensus Problems of Heterogeneous Signed Networks

Yu Ma, Yi Zhang, Jinchao Li, Mingjun Du () and Peng Ji
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Yu Ma: School of Information and Automation Engineering, Qilu University of Technology (Shandong Academy of Science), No. 3501, Daxue Road, Changqing District, Jinan 250353, China
Yi Zhang: School of Information and Automation Engineering, Qilu University of Technology (Shandong Academy of Science), No. 3501, Daxue Road, Changqing District, Jinan 250353, China
Jinchao Li: School of Information and Automation Engineering, Qilu University of Technology (Shandong Academy of Science), No. 3501, Daxue Road, Changqing District, Jinan 250353, China
Mingjun Du: School of Information and Automation Engineering, Qilu University of Technology (Shandong Academy of Science), No. 3501, Daxue Road, Changqing District, Jinan 250353, China
Peng Ji: School of Information and Automation Engineering, Qilu University of Technology (Shandong Academy of Science), No. 3501, Daxue Road, Changqing District, Jinan 250353, China

Mathematics, 2024, vol. 12, issue 10, 1-13

Abstract: This paper aims to study the distributed control problems of heterogeneous signed networks whose communication topologies are undirected. A distributed control protocol is designed based on neighboring state information. With this protocol be employed, the convergence results of the heterogeneous signed network are provided. It is shown that the heterogeneous signed network can achieve the static bipartite consensus (respectively, state stability) if and only if the signed graph is structurally balanced (respectively, unbalanced). The associated convergence analyses can be developed by constructing a suitable Lyapunov function. In addition, two simulation examples are presented to validate the correctness of the obtained results.

Keywords: heterogeneous signed network; distributed protocol; static bipartite consensus; structural balance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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