A new Lyapunov function for stability of time-varying nonlinear perturbed systems

In this paper, global and local uniform asymptotic stability of perturbed dynamical systems is studied by using Lyapunov techniques. The restriction about the perturbed term is that the perturbation is bounded by an integrable function under the assumption that the nominal system is globally uniformly asymptotically stable. We use a new Lyapunov function to obtain a global uniform asymptotical stability of some perturbed systems.