Quasi-Interval Bipartite Consensus Problems on Discrete-Time Signed Networks
In this paper, discrete-time signed networks with cooperative and antagonistic interactions are considered in the presence of time-varying topologies. A separation approach is proposed such that the cooperations and antagonisms can be clearly distinguished. It is shown that given the repeated joint strong connectivity, signed networks can achieve bipartite consensus (respectively, stability) if and only if the repeated joint structural balance (respectively, unbalance) are ensured. Furthermore, when only joint spanning tree condition is satisfied, quasi-interval bipartite consensus (respectively, stability) holds if and only if the repeated joint structural balance (respectively, unbalance) can be guaranteed for the signed digraphs formed by only these joint root nodes. The simulation tests are included to verify the effectiveness of our obtained results.
KeywordsDiscrete-timedynamics Signed networks Time-varying topology Repeated joint structural balance
This work was supported in part by the National Natural Science Foundation of China (61873013, 61473010, 61473015, 61520106010), in part by the Beijing Natural Science Foundation (4162036), and in part by the Fundamental Research Funds for the Central Universities.
- 1.L. Jure, H. Daniel, K. Jon, Signed networks in social media, in Proceedings of the 28th International Conference on Human Factors in Computing Systems, Atlanta, GA, USA, April 2010, pp. 1361–1370Google Scholar
- 5.J. Hu, W. Zheng, Bipartite consensus for multi-agent systems on directed signed networks, in Proceeding of the 52nd IEEE Conference on Decision and Control (Florence, Italy, 2013), pp. 3452–3456Google Scholar
- 15.J.M. Hendrickx, A lifting approach to models of opinion dynamics with antagonisms, in Proceedings of the IEEE Conference on Decision and Control (Los Angeles, CA, USA, 2014), pp. 2118–2123Google Scholar
- 16.D. Meng, Convergence analysis of directed signed networks via an M-matrix approach. Int. J. Control, https://doi.org/10.1080/00207179.2017.1294263
- 17.D. Cartwright, F. Harary, Structural balance: a generalization of Heider’s theory. Psychol. Rev. 63(5), 9–25 (1977)Google Scholar
- 18.R.A. Horn, C.R. Johnson, Matrix Analysis (Cambridge University Press, 1985)Google Scholar
- 19.D. Meng, Z. Meng, Y. Hong, A state transition matrix-based approach to separation of cooperations and antagonisms in opinion dynamics. arXiv:1705.04430