Nonlinear Dynamics

, Volume 87, Issue 1, pp 207–218 | Cite as

Practical bipartite synchronization via pinning control on a network of nonlinear agents with antagonistic interactions

  • Shidong Zhai
  • Qingdu Li
Original Paper


This paper studies the synchronization phenomena in a network of heterogeneous nonlinear systems over signed graph, which can be considered as the perturbation of a network of homogeneous nonlinear systems. Assume that the signed graph is structurally balanced, the nonlinear system satisfies one-sided Lipschitz condition, and a leader pins a subset of agents. Under some proper initial conditions of the leader, we derive some conditions under which bipartite synchronization error can be kept arbitrary small by choosing a proper pining scheme. This property is called practical pinning bipartite synchronization as an alternative synchronization notion for network of heterogeneous nonlinear systems over signed graph. Finally, we present a numerical example to illustrate the effectiveness of the obtained results.


Bipartite synchronization Heterogeneous nonlinear systems Pinning control 


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Research Center of Analysis and Control for Complex Systems, Key Laboratory of Industrial Internet of Things and Networked Control, Ministry of EducationChongqing University of Posts and TelecommunicationsChongqingChina

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