Lyapunov functionals and asymptotic stability in infinite delay systems (Q1384458)

Systems with infinite delay are considered. Lyapunov's direct method is used to derive sufficient conditions for uniform asymptotic stability. The main tool is a seminorm having a fading memory with respect to the norm of the space of initial functions. By using this norm, the authors establish a Lyapunov functional with an upper bound larger that those traditionally given. That approach allows us to unify some well-known results. Relevant examples are given.