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Robust Control Theory in Hilbert Space

  • Book
  • © 1998

Overview

Authors:
  1. Avraham Feintuch

    1. Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel

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  • The necessary operator theory is developed from first principles - The book is as self-contained as possible - All competition is aimed at the engineering community; this book is aimed at mathematicians interested in the potential applications and extensions of their work

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

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xv
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  2. Basic Hilbert Space Theory

    • Avraham Feintuch
    Pages 1-18

  3. Operator Theoretic Preliminaries

    • Avraham Feintuch
    Pages 19-31

  4. A Distance Formula and Some Consequences

    • Avraham Feintuch
    Pages 33-54

  5. Factorization Theorems

    • Avraham Feintuch
    Pages 55-75

  6. Linear Systems

    • Avraham Feintuch
    Pages 77-86

  7. Stabilization

    • Avraham Feintuch
    Pages 87-115

  8. Uniform Optimal Control

    • Avraham Feintuch
    Pages 117-142

  9. Robustness of Time-Varying Systems

    • Avraham Feintuch
    Pages 143-164

  10. The Gap Metric and Internal Stability

    • Avraham Feintuch
    Pages 165-185

  11. Robust Stabilization in the Gap Metric

    • Avraham Feintuch
    Pages 187-205

  12. Orthogonal Embedding of Time-Varying Systems

    • Avraham Feintuch
    Pages 207-216

  13. Back Matter

    Pages 217-225
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Avraham Feintuch

Bibliographic Information

  • Book Title: Robust Control Theory in Hilbert Space

  • Authors: Avraham Feintuch

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-1-4612-0591-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Hardcover ISBN: 978-0-387-98291-5Published: 20 November 1997

  • Softcover ISBN: 978-1-4612-6829-1Published: 30 September 2012

  • eBook ISBN: 978-1-4612-0591-3Published: 06 December 2012

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: XV, 228

  • Topics: Calculus of Variations and Optimal Control; Optimization

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