Cluster synchronization for delayed Lur'e dynamical networks based on pinning control

Authors:
Ting Wang;Tao Li;Xin Yang;Shumin Fei
Affiliations:
Key Laboratory of Measurement and Control of CSE (School of Automation, Southeast University), Ministry of Education, Nanjing 210096, China;School of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210007, China;School of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210007, China;Key Laboratory of Measurement and Control of CSE (School of Automation, Southeast University), Ministry of Education, Nanjing 210096, China
Venue:
Neurocomputing
Year:
2012

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Abstract

In this paper, the problem on cluster synchronization is investigated for continuous/discrete-time Lur'e type dynamical networks by using pinning control strategy. Through combining Jensen inequality with reciprocal convex technique, some sufficient conditions are derived to ensure the cluster synchronization for the addressed networks if the designed linear feedback controller is employed to every cluster. Moreover, the problems of the controller design can be converted into solving a series of linear matrix inequalities (LMIs), which can help reduce the computation complexity. Finally, three numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.