In this paper, by employing
the theory of systems of functional differential inequalities, a very general
comparison theorem for functional differential systems in the context of vector
Lyapunov functions is developed. Furthermore, this comparison theorem has
been applied to derive sufficient conditions for stability of the equilibrium
state of the functional differential systems under structural perturbations
caused by the interactions among the states of the system. Finally, the role of
comparison theorem in the framework of vector Lyapunov functions has been
demonstrated by investigating the stability analysis of hereditary interconnected
systems.
