Comparison result and Lyapunov stability criteria with initial time difference

Abstract

We investigate the qualitative behaviour of a perturbed differential system that differs in initial position and initial time with respect to the unperturbed differential system. We compare the classical notion of stability to the notion of initial time difference stability. We present a comparison result which again gives the null solution a central role in the comparison differential system when establishing initial time difference stability of the perturbed differential system with respect to the unperturbed system.