High-Order Analysis Of Critical Stability Properties of Linear Time-Delay Systems

In this paper we study stability properties of linear time-delay systems with commensurate delays. We investigate specifically the asymptotic behavior of the critical characteristic zeros of time-delay systems on the imaginary axis. This behavior determines whether the imaginary zeros cross from one half plane into another, and hence plays a critical role in determining the stability of a time-delay system. We emphasize in particular the second-order asymptotic properties, which, together with earlier results on first-order analysis, provide a more complete characterization of the zero asymptotic behavior.