Bipartite Consensus Problems for Directed Signed Networks with External Disturbances

Baoyu Huo, Jian Ma and Mingjun Du ()
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Baoyu Huo: The School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Science), Jinan 250353, China
Jian Ma: The School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Science), Jinan 250353, China
Mingjun Du: The School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Science), Jinan 250353, China

Mathematics, 2023, vol. 11, issue 23, 1-16

Abstract: The intention of this paper is to explore the distributed control issues for directed signed networks in the face of external disturbances under strongly connected topologies. A new class of nonsingular transformations is provided by introducing an output variable, with which the consensus can be equivalently transformed into the output stability regardless of whether the associated signed digraphs are structurally balanced or not. By taking advantage of the standard robust H ∞ control theory, the bipartite consensus and state stability results can be built for signed networks under structurally balanced and unbalanced conditions, respectively, in which the desired disturbance rejection performances can also be satisfied. Furthermore, the mathematical expression can be given for the terminal states of signed networks under the influence of external disturbances. In addition, two simulations are presented to verify the correctness of our developed results.

Keywords: distributed control; external disturbance; mathematical expression; signed network; structural balance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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