Nonlinear Dynamics

, Volume 83, Issue 1–2, pp 739–749 | Cite as

Cluster synchronization in nonlinear complex networks under sliding mode control

Original Paper


This paper investigates the cluster synchronization for network of nonlinear systems via differential mean value theorem method and sliding mode control strategy. Because of the existence of the nonlinear dynamics, the differential mean value theorem method is used to transform the nonlinear error complex network system into a linear parameter-varying system. Since the robustness to the uncertainties of the sliding mode, we can deal with the linear parameter-varying system which contains the time-varying mismatched uncertainties by applying the sliding mode control strategy through the equivalent transformation. In addition, appropriate linear matrix inequality stability condition by the Lyapunov method is derived such that each subsystem in the new sliding mode is completely invariant to both matched and mismatched uncertainties. Finally, simulation example is shown to illustrate the effectiveness of the proposed method.


Cluster synchronization Differential mean value theorem Time-varying mismatched uncertainties Sliding mode control 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Institute of System ScienceNortheastern UniversityShenyangChina
  2. 2.Key Laboratory of Networked Control SystemsChinese Academy of SciencesBeijingChina

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