Nonlinear Dynamics

, Volume 48, Issue 4, pp 409–416 | Cite as

Stability analysis of linear fractional differential system with multiple time delays

  • Weihua Deng
  • Changpin LiEmail author
  • Jinhu Lü
Original Article


In this paper, we study the stability of n-dimensional linear fractional differential equation with time delays, where the delay matrix is defined in (R +)n×n. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. As its an application, we apply our theorem to the delayed system in one spatial dimension studied by Chen and Moore [Nonlinear Dynamics 29, 2002, 191] and determine the asymptotically stable region of the system. We also deal with synchronization between the coupled Duffing oscillators with time delays by the linear feedback control method and the aid of our theorem, where the domain of the control-synchronization parameters is determined.


Delay Duffing oscillator Linear fractional differential system Stability Synchronization 


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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouChina
  2. 2.Department of MathematicsShanghai UniversityShanghaiChina
  3. 3.Key Laboratory of Systems and Control, Institute of Systems ScienceAcademy of Mathematics and Systems Science, Chinese Academy of SciencesBeijingChina

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