Robust Control Theory in Hilbert Space

  • Avraham Feintuch

Part of the Applied Mathematical Sciences book series (AMS, volume 130)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Avraham Feintuch
    Pages 1-18
  3. Avraham Feintuch
    Pages 19-31
  4. Avraham Feintuch
    Pages 33-54
  5. Avraham Feintuch
    Pages 55-75
  6. Avraham Feintuch
    Pages 77-86
  7. Avraham Feintuch
    Pages 87-115
  8. Avraham Feintuch
    Pages 117-142
  9. Avraham Feintuch
    Pages 143-164
  10. Avraham Feintuch
    Pages 165-185
  11. Avraham Feintuch
    Pages 187-205
  12. Avraham Feintuch
    Pages 207-216
  13. Back Matter
    Pages 217-225

About this book

Introduction

Motivation The latest texts on linear systems for engineering students have begun incorpo­ rating chapters on robust control using the state space approach to HOC control for linear finite dimensional time-invariant systems. While the pedagogical and computational advantages of this approach are not to be underestimated, there are, in my opinion, some disadvantages. Among these disadvantages is the narrow viewpoint that arises from the amputation of the finite dimensional time-invariant case from the much more general theory that had been developed using frequency domain methods. The frequency domain, which occupied center stage for most of the develop­ ments of HOC control theory, presents a natural context for analysis and controller synthesis for time-invariant linear systems, whether of finite or infinite dimen­ sions. A fundamental role was played in this theory by operator theoretic methods, especially the theory of Toeplitz and skew-Toeplitz operators. The recent lecture notes of Foias, Ozbay, and Tannenbaum [3] display the power of this theory by constructing robust controllers for the problem of a flexible beam. Although controller synthesis depends heavily on the special computational ad­ vantages of time-invariant systems and the relationship between HOC optimization and classical interpolation methods, it turns out that the analysis is possible without the assumption that the systems are time-invariant.

Keywords

Hilbert space Operator theory control control theory optimal control robust control stability stabilization

Authors and affiliations

  • Avraham Feintuch
    • 1
  1. 1.Department of Mathematics and Computer ScienceBen-Gurion University of the NegevBeer-ShevaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0591-3
  • Copyright Information Springer Science+Business Media New York 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6829-1
  • Online ISBN 978-1-4612-0591-3
  • Series Print ISSN 0066-5452
  • About this book