Distributed Control Problems of Second-Order Directed Signed Networks Based on Sampled Data

In this study, the bipartite consensus problem of directed signed network based on sampled data is studied. A control protocol for second-order signed network is proposed, which is based on sampling data. By leveraging principles of the Laplacian matrix and graph theory, the protocol is derived, and the necessary and sufficient conditions for achieving bipartite consensus and state stability are identified. The research findings suggest that bipartite consensus can be reached in structurally balanced network topologies with the correct choice of sampling period and parameters, whereas state stability is achievable in structurally unbalanced configurations. In addition, simulation examples are used to verify the accuracy of the derived results.