An Analytical Eigenvalue Assignment of Linear Time-Delay Systems Using Lambert W Function

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 epectively and for both of them, sufficient conditions for eigenvalue assignment are proposed.