Some remarks on transformations used for stability and robust stability analysis of time-delay systems

It is quite common in stability analysis of time-delay systems to make special transformations of the system under investigation in order to get stability conditions which depend on values of delays. We discuss additional conditions for the asymptotic stability of the transformed system which do not appear for that of the original system. These conditions are results of the transformations and may be expressed in the form of specific restrictions imposed on spectrum location of some system matrices.