Analysis of Control System with Delay Using the Lambert Function

  • Irma Ivanovienė
  • Jonas Rimas
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 403)


The mathematical model of the mutual synchronization system, having ring form structure and composed of n (n ∈ N) oscillators, is investigated. The mathematical model of the system is the matrix differential equation with delayed argument. The solution of the matrix differential equation with delayed argument is obtained applying the Lambert function method. Using obtained solution, the transients in the system are examined. The results of calculations, received by the Lambert function method, are compared with the results, obtained by the exact method of consequent integration.


synchronization system differential equations delayed arguments Lambert function 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Irma Ivanovienė
    • 1
  • Jonas Rimas
    • 1
  1. 1.Department of Applied MathematicsKaunas University of TechnologyKaunasLithuania

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