Synchronization Control of Riemann-Liouville Fractional Competitive Network Systems with Time-varying Delay and Different Time Scales

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Abstract

This paper is concerned with a class of Riemann-Liouville fractional-order competitive neural networks with time-varying delay and different time scales. Based on delay-partitioning approach, we construct two suitable Lyapunov functionals including fractional integral terms, respectively, and avoid computing their fractional-order derivatives to derive the synchronization conditions. The sufficient conditions are proposed to ensure the complete synchronization between fractional-order response system and fractional-order derive system. By solving the algebraic equalities or linear matrix inequalities (LMIs), the design of the gain matrix of the linear feedback controller can be realized. An illustrative example is also presented to show the validity and feasibility of the theoretical results.

Keywords

Delay-partitioning approach fractional competitive neural networks Lyapunov functional method synchronization control time scales time-varying delay 

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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

  • Hai Zhang
    • 1
  • Miaolin Ye
    • 1
  • Jinde Cao
    • 2
    • 3
    • 4
  • Ahmed Alsaedi
    • 5
  1. 1.School of Mathematics and Computation ScienceAnqing Normal UniversityAnqingChina
  2. 2.School of Mathematics, and Research Center for Complex Systems and Network SciencesSoutheast UniversityNanjingChina
  3. 3.School of Electrical EngineeringNantong UniversityNantongChina
  4. 4.School of Mathematical SciencesShandong Normal UniversityJinanChina
  5. 5.Nonlinear Analysis and Applied Mathematics Research Group, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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