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Global Mittag-Leffler Synchronization of Fractional-Order Neural Networks Via Impulsive Control

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Abstract

This paper aims at analyzing the impulsive synchronization of fractional-order neural works. Firstly, in view of control theory, by constructing a suitable impulsive response system with the designed controller, the synchronization error system between the drive system and the corresponding response system is given. Afterwards, based on the theory of impulsive differential equation, the theory of fractional differential equation, Lyapunov direct method, and inequality techniques, some effective sufficient criteria are established to guarantee the global Mittag-Leffler stability for the synchronization error system. Finally, several simulation examples are designed to demonstrate the effectiveness and feasibility of the obtained results.

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Acknowledgements

This work was supported by the Qatar National Research Fund, a member of the Qatar Foundation, through the National Priorities Research Program under Grant NPRP 9-166-1-031, by the National Natural Science Foundation of China under Grants 61374078, 61773004 and 11501065, and in part by the Chongqing Research Program of Basic Research and Frontier Technology of cstc2015jcyjBX0052.

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Authors and Affiliations

  1. Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, People’s Republic of China

    Xujun Yang & Chuandong Li

  2. Texas A&M University at Qatar, Doha, 23874, Qatar

    Tingwen Huang

  3. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074, People’s Republic of China

    Qiankun Song

  4. Department of Computer Science, Chongqing University of Education, Chongqing, 400067, People’s Republic of China

    Junjian Huang

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  1. Xujun Yang
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  2. Chuandong Li
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  3. Tingwen Huang
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  4. Qiankun Song
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  5. Junjian Huang
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Correspondence to Chuandong Li.

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Yang, X., Li, C., Huang, T. et al. Global Mittag-Leffler Synchronization of Fractional-Order Neural Networks Via Impulsive Control. Neural Process Lett 48, 459–479 (2018). https://doi.org/10.1007/s11063-017-9744-x

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