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...

A book is never the sole accomplishment of the authors. It is built on the foun- dation of established mathematics, and it benefits from current developments within the mathematical community. Many colleagues have contributed ideas, comments, and corrections to this volume. There are, first of all, our students C. Bauer, G. Grammel, 1. Greger, S. Grtinvogel, G. Hackl, and D. Szolnoki in Augs- burg, and E. Joseph, R.-G. Lai, S. Lin, C.-M. Ou, and H. Wang in Ames. We have received comments from, among others, L. Arnold, V. Ayala, K. Grasse, D. Hinrichsen, R. Johnson, Y. Latushkin, J.L. Massera,...