Stability and performance of first-order linear time-delay feedback systems: An eigenvalue approach

Linear time-delay systems with transcendental characteristic equations have infinitely many eigenvalues which are generally hard to compute completely. however,the spectrum of first-order linear time-delay systems can be analyzed with the lambert function. this paper studies the stability and state feedback stabilization of first-order linear time-delay system in detail via the lambert function. the main issues concerned are the rightmost eigenvalue locations,stability robustness with respect to delay time,and the response performance of the closed-loop system. examples and simulations are presented to illustrate the analysis results. copyright © 2011 shu-an he and i-kong fong.