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R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey and D. E. Knuth, “On the Lambert W function,” Advances in Computational Mathematics, Vol. 5, No. 4, 1996, pp. 329-359. doi:10.1007/BF02124750

has been cited by the following article:

• TITLE: PID Stabilization of Linear Neutral Time-Delay Systems in a Numerical Approach

  AUTHORS: Hassan Farokhi Moghadam, Nastaran Vasegh, Seyed Zeinolabedin Moussavi

  KEYWORDS: Neutral Time-Delay Systems; PID Controller; Stability; Iterative Method; Rightmost Characteristic Root; Nyquist Plot

  JOURNAL NAME: Intelligent Control and Automation, Vol.3 No.4, November 28, 2012

  ABSTRACT: In this paper, the stabilization of neutral time-delay systems is investigated. An efficient numerical approach is presented in an algorithm to establish results so that stability of such systems is achieved and stabilizing PID parameters are determined directly. It is based on determining the rightmost characteristic roots and Nyquist plot. The Newton-Raphson’s iterative method based on Lambert W function is used for the calculation of these stabilizing roots directly from the closed-loop characteristic equation of the neutral time-delay system and then stability is checked by Nyquist plot and step response of closed-loop system. Two numerical examples are included to illustrate the effectiveness of the proposed approach.