An analytical eigenvalue assignment of linear time-delay systems using Lambert W function

Nemati M., Hashemzadeh F., Baradarannia M., Ghiasi A.

5th International Conference on Control, Instrumentation, and Automation, ICCIA 2017, Shiraz, Iran, 21 - 23 November 2017, vol.2018-January, pp.222-227 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 2018-January
  • Doi Number: 10.1109/icciautom.2017.8258682
  • City: Shiraz
  • Country: Iran
  • Page Numbers: pp.222-227
  • Keywords: eigenvalue assignment, Lambert W, time-delay
  • Istanbul Technical University Affiliated: No


A new method is presented in this article to control linear time-delay systems using Lambert W function. The absence of a sufficient proof for using matrix Lambert W function in controlling time-delay systems has frustrated researchers. It is a well-established fact that unlike Lambert W Function, the matrix version still lacks the proof, which would guarantee the validity of finding the right-most eigenvalue of linear time-delay systems using this function. This paper presents a new approach in which, a system from any order is forced to use scalar Lambert W function instead of unreliable matrix version. This article studies systems with input delay and state delay respectively and for both of them, sufficient conditions for eigenvalue assignment are proposed.