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Asymptotic Behavior of Dynamical and Control Systems under Pertubation and Discretization

  • Book
  • © 2002

Overview

Authors:
  1. Lars Grüne
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1783)

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Table of contents (13 chapters)

  1. Front Matter

    Pages N2-IX
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  2. 1. Introduction: Dynamics, Perturbation and Discretization

    • Lars Grüne
    Pages 1-12

  3. 2. Setup and Preliminaries

    • Lars Grüne
    Pages 13-25

  4. 3. Strongly Attracting Sets

    • Lars Grüne
    Pages 27-68

  5. 4. Weakly Attracting Sets

    • Lars Grüne
    Pages 69-112

  6. 5. Relation between Discretization and Perturbation

    • Lars Grüne
    Pages 113-136

  7. 6. Discretizations of Attracting Sets

    • Lars Grüne
    Pages 137-156

  8. 7. Domains of Attraction

    • Lars Grüne
    Pages 157-194

  9. Appendix A: Viscosity Solutions

    • Lars Grüne
    Pages 195-200

  10. Appendix B: Comparison Functions

    • Lars Grüne
    Pages 201-205

  11. Appendix C: Numerical Examples

    • Lars Grüne
    Pages 207-217

  12. Notation

    • Lars Grüne
    Pages 219-220

  13. References

    • Lars Grüne
    Pages 221-227

  14. Index

    • Lars Grüne
    Pages 229-231

  15. Back Matter

    Pages 233-235
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Keywords

About this book

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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