Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization Dynamics Perturbation and Discretization Setup and Preliminaries Strongly Attracting Sets Weakly Attracting Sets Relation between Discretization and Perturbation Discretizations of Attractive Sets Domains of Attraction Appendices. Viscosity Solutions. Comparison Functions. Numerical Examples. This book provides an approach to the study of perturbation and discretization effects on the long time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets attractors asumptotically controllable sets and their respective domains of attractions and reachable sets. Combining robust stability concepts from nonlinear control theory techniques from optimal control and differential games and methods from nonsmooth analysis both qualitative and quantitative results are obtained and new algorithms are developed analyzed and illustrated by examples.