On the asymptotic stability for functional differential equations by Lyapunov functionals

Sufficient conditions for the asymptotic stability and uniform asymptotic stability of the zero solution of nonautonomous FDE's with finite delays are given by Lyapunov-Krasovskii functionals with negative semidefinite derivatives. The results are applied to the equation x'(t) = -a(t)x(t) + b(t) integral(t-h)(t) lambda(s)x(s) ds, (a(t) greater than or equal to 0), where a, b : R+ --> R+, lambda: [-h, infinity) --> R are continuous functions.