ABSTRACT
Researchers have introduced an axiomatic definition of phase space for systems with infinite delay (SID) (after-effect), and at the same time initiated a unified approach to the analysis of a such systems. Lyapunov’s direct method based on Lyapunov-Razumikhin functions has also been used in the stability analysis of SID. In this case the corresponding definitions are modified to take account of the concept of stability developed for Rn in a B space defined by specific hypotheses. This chapter gives definitions. It discusses the relationships between stability in Rn and stability in B, and characterizes several properties of V functions in terms of special types of comparison functions.
