Analysis of Control System with Delay Using the Lambert Function
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.
Keywordssynchronization system differential equations delayed arguments Lambert function
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