Uniform asymptotic stability in infinite delay systems (Q1322315)

Using the technique of Lyapunov functionals, the author derives conditions for uniform asymptotic stability of infinite delay functional differential systems of the type \(x'(t)= f(t,x_ t)\), where \(x(t)\in \mathbb{R}^ n\) and \(x_ t(s)= x(t+ s)\), \(s\leq 0\). Integro-differential equations with infinite delay are considered as illustration of the stability results obtained.