Robust Control Theory in Hilbert Space (Hardcover)

Avraham Feintuch

ISBN 10: 0387982914 / ISBN 13: 9780387982915

Editore: Springer-Verlag New York Inc., New York, NY, 1997

Hardcover. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9780387982915

Riassunto:

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.

Contenuti: 1 Basic Hilbert Space Theory.- 2 Operator Theoretic Preliminaries.- 3 A Distance Formula and Some Consequences.- 4 Factorization Theorems.- 5 Linear Systems.- 6 Stabilization.- 7 Uniform Optimal Control.- 8 Robustness of Time-Varying Systems.- 9 The Gap Metric and Internal Stability.- 10 Robust Stabilization in the Gap Metric.- 11 Orthogonal Embedding of Time-Varying Systems.

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Titolo: Robust Control Theory in Hilbert Space (...
Casa editrice: Springer-Verlag New York Inc., New York, NY
Data di pubblicazione: 1997
Legatura: Hardcover
Condizione: new