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Synchronization for a Class of Fractional-order Linear Complex Networks via Impulsive Control

  • Na Liu
  • Jie Fang
  • Wei Deng
  • Zhen-Jun Wu
  • Guo-Qiang Ding
Regular Papers Control Theory and Applications
  • 15 Downloads

Abstract

Up to now, the research topic about fractional-order complex networks is mainly focused on the synchronization. In this paper, synchronization for a class of fractional-order linear complex networks is realized via impulsive control. The general expression of solution for a fractional-order impulsive error system is deduced by utilizing iteration algorithm. Some inequality conditions are established to guarantee that the largest Lyapunov exponents of each node are negative, which means that the corresponding error system is asymptotic stable and synchronization is realized. It is the first time to achieve the synchronization of fractional-order systems based on the largest Lyapunov exponent. Finally, examples are present to illustrate the validity and effectiveness of proposed conclusions. Numerical simulations also indicate that the fractional-order parameter has a great influence on the largest Lyapunov exponent, although it is not reflected in the theoretical analysis.

Keywords

Complex networks fractional-order impulsive control synchronization 

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Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Na Liu
    • 1
  • Jie Fang
    • 1
  • Wei Deng
    • 1
  • Zhen-Jun Wu
    • 1
  • Guo-Qiang Ding
    • 1
  1. 1.School of Electric and Information EngineeringZhengzhou University of Light IndustryZhengzhou, Henan ProvinceChina

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