Novel criteria for stability and convergence of solutions for non-autonomous nonlinear systems

In this paper, we give a new integral inequality which is used to study the asymptotic behaviour of solutions for a class of nonlinear dynamic systems with small perturbation using a numerical approach. We provide some new results on the stability of perturbed systems where necessary and sufficient condition is derived. We show that the perturbed nonlinear system can be globally uniformly practically asymptotically stable provided that the bound of perturbation is small enough. A numerical example is presented to illustrate the validity of the main result.