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Robust Control Theory in Hilbert Space : Applied Mathematical Sciences - Avraham Feintuch

Robust Control Theory in Hilbert Space

Applied Mathematical Sciences

Hardcover Published: 20th November 1997
ISBN: 9780387982915
Number Of Pages: 228

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This book presents an operator theoretic approach to robust control analysis for linear time-varying systems. It emphasizes the conceptual similarity with the H control theory for time-invariant systems and at the same time clarifies the major difficulties confronted in the time varying case. The necessary operator theory is developed from first principles and the book is as self-contained as possible. After presenting the necessary results from the theories of Toeplitz operators and nest algebras, linear systems are defined as input- output operators and the relationship between stabilization and the existance of co-prime factorizations is described. Uniform optimal control problems are formulated as model-matching problems and are reduced to four block problems. Robustness is considered both from the point of view of fractional representations and the "time varying gap" metric, and the relationship between these types of uncertainties is clarified. The book closes with the solution of the orthogonal embedding problem for time varying contractive systems. This book will be useful to both mathematicians interested in the potential applications of operator theory in control and control engineers who wish to deal with some of the more mathematically sophisticated extension of their work.

Preface
Basic Hilbert Space Theoryp. 1
Operator Theoretic Preliminariesp. 19
A Distance Formula and Some Consequencesp. 33
Factorization Theoremsp. 55
Linear Systemsp. 77
Stabilizationp. 87
Uniform Optimal Controlp. 117
Robustness of Time-Varying Systemsp. 143
The Gap Metric and Internal Stabilityp. 165
Robust Stabilization in the Gap Metricp. 187
Orthogonal Embedding of Time-Varying Systemsp. 207
Indexp. 217
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387982915
ISBN-10: 0387982914
Series: Applied Mathematical Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 228
Published: 20th November 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.54