Asymptotic Behavior of Dynamical and Control Systems under Perturbation and Discretization

Lars Grüne (auth.)3540433910, 9783540433910

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.

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Table of contents :
1. Introduction: Dynamics, Perturbation and Discretization….Pages 1-12
2. Setup and Preliminaries….Pages 13-25
3. Strongly Attracting Sets….Pages 27-68
4. Weakly Attracting Sets….Pages 69-112
5. Relation between Discretization and Perturbation….Pages 113-136
6. Discretizations of Attracting Sets….Pages 137-156
7. Domains of Attraction….Pages 157-194
Appendix A: Viscosity Solutions….Pages 195-200
Appendix B: Comparison Functions….Pages 201-205
Appendix C: Numerical Examples….Pages 207-217
Notation….Pages 219-220
References….Pages 221-227
Index….Pages 229-231