Nonlinear Dynamics

, Volume 94, Issue 4, pp 3101–3116 | Cite as

Synchronization of fractional-order complex dynamical network with random coupling delay, actuator faults and saturation

  • P. Selvaraj
  • R. SakthivelEmail author
  • O. M. KwonEmail author
Original Paper


This paper examines the synchronization problem of fractional-order complex dynamical networks (FCDNs) against input saturation and time-varying coupling by using a fault-tolerant control scheme. Precisely, the occurrence of coupling delay assumed is considered to be random, which is characterized by stochastic variables that obeys the Bernoulli distribution properties, and the actuator fault values are represented by a normally distributed stochastic random variable. The main aim of this paper is to propose the fault-tolerant fractional-order controller such that for given any initial condition, the state trajectories of considered FCDN are forced to synchronize asymptotically to the reference node. Based on the linear matrix inequality technique and Lyapunov stability theorem, a new set of sufficient conditions is established to not only guarantee mean-square asymptotic synchronization of the resulting closed-loop system but also cover the issues of actuator saturation and actuator faults. Moreover, the obtained sufficient conditions can help to enlarge the estimation about the domain of attraction for the closed-loop system. Finally, to show the advantages and effectiveness of the developed control design, numerical simulations are carried out on both Lorenz and Chen type FCDNs.


Complex dynamical networks Fractional time delay systems Synchronization Saturation effect Stochastic actuator fault 



This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2016R1D1A1A09917886) and by the Brain Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2017M3C7A1044815).

Compliance with ethical standards

Conflicts of interest

The authors declare that there is no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Electrical EngineeringChungbuk National UniversityCheongjuSouth Korea
  2. 2.Department of MathematicsBharathiar UniversityCoimbatoreIndia

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