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.