Nonlinear Dynamics

, Volume 70, Issue 1, pp 475–479 | Cite as

Studying on the stability of fractional-order nonlinear system

  • Ling-Dong Zhao
  • Jian-Bing Hu
  • Jian-An Fang
  • Wen-Bing Zhang
Original Paper


In this paper, we study the properties of the Mittag–Leffler function and propose an approach for calculating the maximum norm of eigenvalue of Jacobian matrix of nonlinear system. Then a simple approach is proposed for judging the stability of fractional nonlinear system. Based on the approach, the maximum decay rate of fractional nonlinear system can be calculated. Finally, some examples are provided to illustrate the approach.


Fractional Mittag–Leffler Stability Decay rate Jacobian matrix 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Ling-Dong Zhao
    • 1
    • 2
  • Jian-Bing Hu
    • 2
  • Jian-An Fang
    • 1
  • Wen-Bing Zhang
    • 1
  1. 1.College of Information Science and TechnologyDonghua UniversityShanghaiP.R. China
  2. 2.School of Electronics & InformationNantong UniversityNantongP.R. China

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