Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue Approach

Linear time-delay systems with transcendental characteristic equations have infinitelymany 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.