193
Views
2
CrossRef citations to date
0
Altmetric
Articles

Algebraic criteria for structure identification and behaviour analysis of signed networks

, &
Pages 2333-2347 | Received 19 Jul 2018, Accepted 05 Aug 2019, Published online: 20 Aug 2019

References

  • Acemoglu, D., & Ozdaglar, A. (2011). Opinion dynamics and learning in social networks. Dynamic Games and Applications, 1(1), 3–49.
  • Altafini, C. (2013). Consensus problems on networks with antagonistic interactions. IEEE Transactions on Automatic Control, 58(4), 935–946.
  • Beineke, L. W., & Harary, F. (1978). Consistency in marked digraphs. Journal of Mathematical Psychology, 18, 260–269.
  • Cartwright, D., & Harary, F. (1956). Structural balance: A generalization of Heider's theory. Psychological Review, 63(5), 277–292.
  • Cheng, L., Hou, Z., & Tan, M. (2014). A mean square consensus protocol for linear multi-agent systems with communication noises and fixed topologies. IEEE Transactions on Automatic Control, 59, 261–267.
  • Cheng, L., Wang, H., Hou, Z., & Tan, M. (2016). Reaching a consensus in networks of high-order integral agents under switching directed topologies. International Journal of Systems Science, 47(8), 1966–1981.
  • Du, M., Ma, B., & Xie, W. (2017). Algebraic criteria for consensus problems of signed directed networks. In Proceeding of 13th Chinese intelligent systems conference, Mudanjiang, China (pp. 451–460).
  • Eagle, N., Macy, M, & Claxton, R. (2010). Network diversity and economic development. Science, 328(5981), 1029–1031.
  • Fan, M., Zhang, H., & Wang, M. (2014). Bipartite flocking for multi-agent systems. Communications in Nonlinear Science and Numerical Simulation, 19(9), 3313–3322.
  • Harary, F. (1953). On the notion of balance of a signed graph. The Michigan Mathematical Journal, 2, 143–146.
  • Harary, F., & Kabell, J. A. (1980). A simple algorithm to detect balance in signed graphs. Mathematical Social Sciences, 1, 131–136.
  • Hu, H., Wen, G., Yu, W., Xuan, Q., & Chen, G. (2018). Swarming behavior of multiple Euler–Lagrange systems with cooperation-competition interactions: An auxiliary system approach. IEEE Transactions on Neural Networks and Learning Systems, 29(11), 5726–5737.
  • Hu, J., Xiao, Z., Zhou, Y., & Yu, J. (2013). Formation control over antagonistic networks. In Proceeding of the Chinese control conference, Xi'an, China (pp. 6879–6884).
  • Jackson, M. O., Rogers, B. W., & Zenou, Y. (2017). The economic consequences of social-network structure. Journal of Economic Literature, 55(1), 49–95.
  • Jadbabaie, A., Lin, J., & Morse, A. S. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 48(6), 988–1001.
  • Jiang, Y., & Jiang, J. (2015). Diffusion in social networks: A multiagent perspective. IEEE Transactions on Systems, Man and Cybernetics: Systems, 45(2), 198–213.
  • Jiang, Y., Zhang, H., & Chen, J. (2017). Sign-consensus of linear multi-agent systems over signed directed graphs. IEEE Transactions on Industrial Electronics, 64(6), 5075–5083.
  • Lazer, D (2011). Networks in political science: Back to future. PS: Political Science and Politics, 44(1), 61–68.
  • Li, Z., & Jia, Y. (2009). Algebraic criteria for consensus problems of continuous-time network systems. International Journal of Control, 82(4), 643–658.
  • Liu, Y., & Jia, Y. (2012a). H∞ consensus control for multi-agent systems with linear coupling dynamics and communication delays. International Journal of Systems Science, 43(1), 50–62.
  • Liu, Y., & Jia, Y. (2012b). An iterative learning approach to formation control of multi-agent systems. Systems and Control Letters, 61(1), 148–154.
  • Luo, X., & Jia, Y. (2011). Decentralised control for formation reorganisation of multi-agent systems using a virtual leader. International Journal of Systems Science, 42(1), 171–182.
  • Ma, H., Liu, D., Wang, D., & Luo, B. (2016). Bipartite output consensus in networked multi-agent systems of high-order power integrators with signed digraph and input noises. International Journal of Systems Science, 47(13), 3116–3131.
  • Meng, D. (2017). Bipartite containment tracking of signed networks. Automatica, 79, 282–289.
  • Meng, D. (2018). Convergence analysis of directed signed networks via an M-matrix approach. International Journal of Control, 91(4), 827–847.
  • Meng, Z., Anderson, B. D. O., & Hirche, S. (2016). Formation control with mismatched compasses. Automatica, 69, 232–241.
  • Meng, D., Du, M., & Jia, Y. (2016b). Interval bipartite consensus of networked agents associated with signed digraphs. IEEE Transactions on Automatic Control, 61(12), 3755–3770.
  • Meng, D., Jia, Y., & Du, J. (2013). Robust iterative learning protocols for finite-time consensus of multi-agent systems with interval uncertain topologies. International Journal of Systems Science, 46(5), 857–871.
  • Meng, D., Jia, Y., & Du, J. (2015). Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs. International Journal of Control, 88(10), 2074–2085.
  • Meng, D., Jia, Y., & Du, J. (2016c). Finite-time consensus for multiagent systems with cooperative and antagonistic interactions. IEEE Transactions on Neural Networks and Learning Systems, 27(4), 762–770.
  • Meng, D., & Moore, K. L. (2016a). Learning to cooperate: Networks of formation agents with switching topologies. Automatica, 64, 278–293.
  • Meng, Z., Shi, G., Johansson, K. H., Cao, M., & Hong, Y. (2016). Behaviors of networks with antagonistic interactions and switching topologies. Automatica, 73, 110–116.
  • Meng, D., & Zuo, Z. (2016d). Signed-average consensus for networks of agents: A nonlinear fixed-time convergence protocol. Nonlinear Dynamics, 85(1), 155–165.
  • Ning, B., Jin, J., & Zheng, J. (2017). Fixed-time consensus for multi-agent systems with discontinuous inherent dynamics over switching topology. International Journal of Systems Science, 48(10), 2023–2032.
  • Olfati-Saber, R. (2006). Flocking for multi-agent dynamics systems: Algorithms and theory. IEEE Transactions on Automatic Control, 51(3), 401–420.
  • Olfati-Saber, R., & Murray, R. M. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49(9), 1520–1533.
  • Proskurnikov, A. V., Matveev, A. S., & Cao, M. (2016). Opinion dynamics in social networks with hostile aamps: Consensus vs. polarization. IEEE Transactions on Automatic Control, 61(6), 1524–1536.
  • Ren, W., & Beard, R. W. (2005). Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 50(5), 655–661.
  • Riker, W. H. (1982). The two-party system and Duverger's law: An essay on the history of political science. American Political Science Review, 76(4), 753–766.
  • Sontag, E. D. (2007). Monotone and near-monotone biochemical networks. Systems Synthetic Biology, 1(2), 277–292.
  • Tanner, H. G., Jadbabaie, A., & Pappas, G. J. (2007). Flocking in fixed and switching networks. IEEE Transactions on Automatic Control, 52(5), 643–658.
  • Volkmann, L. (1996). Estimations for the number of cycles in a graph. Periodica Mathematica Hungarica, 33(2), 153–161.
  • Wen, G., Duan, Z., Yu, W., & Chen, G. (2013). Consensus of second-order multi-agent systems with delayed nonlinear dynamics and intermittent communications. International Journal of Control, 86(2), 322–331.
  • Wen, G., Wang, H., Yu, X., & Yu, W. (2018). Bipartite tracking consensus of linear multi-agent systems with a dynamic leader. IEEE Transactions on Circuits and System II: Express Briefs, 65(9), 1204–1208.
  • Xia, W., Cao, M., & Johansson, K. H. (2016). Structural balance and opinion separation in trust-mistrust social networks. IEEE Transactions on Control of Networks System, 3(1), 46–56.
  • Yang, Z., Zhang, Q., Jiang, Z., & Chen, Z. (2012). Flocking of multi-agents with time delay. International Journal of Systems Science, 43(11), 2125–2134.
  • Zhang, H., & Chen, J. (2014). Bipartite consensus of general linear multi-agent systems. In Proceeding of American control conference, Portland, USA (pp. 808–812).
  • Zhang, H., & Chen, J. (2017). Bipartite consensus of multi-agent systems over signed graphs: State feedback and output feedback control approaches. International Journal of Robust and Nonlinear Control, 27, 3–14.
  • Zhao, L., Jia, Y., & Yu, J. (2017). Adaptive finite-time bipartite consensus for second-order multi-agent systems with antagonistic interactions. Systems & Control Letters, 102, 22–31.
  • Zuo, Z., & Tie, L. (2016). Distributed robust finite-time nonlinear consensus protocols for multi-agent systems. International Journal of Systems Science, 47(6), 1366–1375.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.