LIAPUNOV FUNCTIONALS AND ASYMPTOTIC STABILITY IN INFINITE DELAY SYSTEMS

Liapunov's direct method is used to give conditions ensuring the unifo rm asymptotic stability in a system of infinite delay differential equ ations. By introducing the concept of a seminorm having a fading memor y with respect to the norm on the space of initial functions, we obtai n a Liapunov functional with an upper bound larger than those traditio nally given. This new approach enables us to unify several well-known theorems in the literature. Examples are provided to illustrate the ap plication of these results.