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

摘要

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