Convergence Rates of Perturbed Attracting Sets with Vanishing Perturbation

We investigate the rate of convergence and the rate of attraction of perturbed attracting sets as the perturbation tends to zero. The perturbation model under consideration is a control system which contains the unperturbed system as zero dynamics. Necessary and sufficient conditions for certain rates of convergence are derived. Several applications especially to numerical approximations are given and a number of examples illustrate the results.