The Use of the Lambert Function Method for Analysis of a Control System with Delays

Authors

  • Irma Ivanovienė Kaunas University of Technology
  • Jonas Rimas Kaunas University of Technology

DOI:

https://doi.org/10.5755/j01.itc.42.4.2484

Keywords:

synchronization system, differential equations, delayed argument, Lambert function

Abstract

The mathematical model of the mutual synchronization system with complete graph structure, composed of n (n∈N) oscillators, is investigated. This mathematical model is defined by the matrix differential equation with delayed argument. The solution of the matrix differential equation with delayed argument is obtained by applying the Lambert W function method. On the base of this solution, the step responses matrix of the synchronization system is defined and the transients in the system are investigated. The results of calculations, received by the Lambert function method, the dde23 method in Matlab and the exact method of consequent integration, are compared.

DOI: http://dx.doi.org/10.5755/j01.itc.42.4.2484

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Published

2013-12-12

Issue

Vol. 42 No. 4 (2013)

Section

Articles

License

Copyright terms are indicated in the Republic of Lithuania Law on Copyright and Related Rights, Articles 4-37.