Synchronization analysis for master and slave system under communication time delay using fractional-order PD\(^{\alpha }\) control



This paper presents a fractional-order PD\(^{\alpha }\) control method for the master and slave system under communication time delay. First, a fractional-order PD\(^{\alpha }\) controller is designed based on the dynamic model of the master and slave system in order to improve the precision and flexibility of operation. Then, the associated characteristic equation for the fractional-order system with time delay is analyzed by taking the time delay as parameter, and the sufficient conditions of asymptotic stability are established to ensure the synchronization of the considered system from eigenvalues point of view. Furthermore, the maximum upper bound of time delay is derived by considering the distribution of roots for characteristic equation. Finally, three numerical simulation examples are given to illustrate the accuracy of conditions and the validity of the novel control architecture.


Master and slave system Synchronization Time delay Fractional-order PD\(^{\alpha }\) controller Eigenvalues 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of AutomationBeijing Institute of TechnologyBeijingPeople’s Republic of China
  2. 2.College of SciencesHebei University of Science and TechnologyShijiazhuangPeople’s Republic of China

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