We consider the asymptotic stability problems by Lyapunov functionals V for a class of functional differential equations with impulses of the form x′(t)=f(t,xt), x∊Rn, t≧t0, t≠tk; △x=Ik(t,x(t−)), t=tk, k∊Z+. Some new asymptotic stability results are presented by using an idea originated by Burton and Makay  and developed by Zhang . We generalize some known results about impulsive functional differential equations in the literature in which we only require the derivative of V to be negative definite on a sequence of intervals In=[sn,ξn] which may or may not be contained in the sequence of impulsive time intervals [tn,tn+1).
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