Convergence rates of perturbed attracting sets with vanishing perturbation

We investigate the rate of convergence and the rate of attraction of pertur bed attracting sets as the perturbation tends to zero. The perturbation mod el under consideration is a control system which contains the unperturbed s ystem as zero dynamics. Necessary and sufficient conditions for certain rat es of convergence are derived. Several applications especially to numerical approximations are given and a number of examples illustrate the results. (C) 2000 Academic Press.