Characterizing invariance properties of linear time-delay systems: The general case

This paper addresses the invariance property of linear time-delay systems in the general case by further exploiting the asymptotic behavior of the critical imaginary roots as well as the singularities of the associated frequency-sweeping curves. The proposed approach allows to overcome the existing limitations in the literature for the explicit characterization of such properties. With this invariance property, a systematic study of the complete stability of linear delay systems can be performed. Some illustrative examples as well as various discussions complete the presentation.