Robust Control Theory in Hilbert Space (Paperback)

Avraham Feintuch

ISBN 10: 146126829X / ISBN 13: 9781461268291

Editore: Springer-Verlag New York Inc., New York, NY, 2012

Riguardo questo articolo

Paperback. 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. 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 9781461268291

Dati bibliografici

• Titolo: Robust Control Theory in Hilbert Space (Paperback)
• Editore: Springer-Verlag New York Inc., New York, NY
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 146126829X
• ISBN 13: 9781461268291
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

An operator theoretic approach to robust control analysis for linear time-varying systems, with the emphasis on the conceptual similarity with the H control theory for time-invariant systems. It clarifies the major difficulties confronted in the time varying case and all the necessary operator theory is developed from first principles, making the book 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 stabilisation and the existence of co-prime factorisations is described. Uniform optimal control problems are formulated as model-matching problems and are reduced to four block problems, while robustness is considered both from the point of view of fractional representations and the "time varying gap" metric, as is the relationship between these types of uncertainties. The book closes with the solution of the orthogonal embedding problem for time-varying contractive systems. As such, this book is useful to both mathematicians and to control engineers.

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.