Linear time-delay systems with transcendental characteristic equations have infinitely many eigenvalues which are generally hard to\r\ncompute completely. However, the spectrum of first-order linear time-delay systems can be analyzed with the Lambert function.\r\nThis paper studies the stability and state feedback stabilization of first-order linear time-delay system in detail via the Lambert\r\nfunction. The main issues concerned are the rightmost eigenvalue locations, stability robustness with respect to delay time, and\r\nthe response performance of the closed-loop system. Examples and simulations are presented to illustrate the analysis results.
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