Abstract
This paper investigates finite-time synchronization of an array of coupled neural networks via discontinuous controllers. Based on Lyapunov function method and the discontinuous version of finite-time stability theory, some sufficient criteria for finite-time synchronization are obtained. Furthermore, we propose switched control and adaptive tuning parameter strategies in order to reduce the settling time. In addition, pinning control scheme via a single controller is also studied in this paper. With the hypothesis that the coupling network topology contains a directed spanning tree and each of the strongly connected components is detail-balanced, we prove that finite-time synchronization can be achieved via pinning control. Finally, some illustrative examples are given to show the validity of the theoretical results.
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This work was jointly supported by the National Natural Science Foundation of China under Grant No. 60874088 and No. 11072059, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20070286003, and the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2009271.
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Shen, J., Cao, J. Finite-time synchronization of coupled neural networks via discontinuous controllers. Cogn Neurodyn 5, 373–385 (2011). https://doi.org/10.1007/s11571-011-9163-z
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DOI: https://doi.org/10.1007/s11571-011-9163-z