Time-Varying Systems and Computations / Edition 1

Time-Varying Systems and Computations / Edition 1

by Patrick DeWilde, Alle-Jan van der Veen
     
 

Time-Varying Systems and Computations is a unique book providing a detailed and consistent exposition of a powerful unifying framework (developed by the authors) for the study of time-variant systems and the computational aspects and problems that arise in this context. While complex function theory and linear algebra provide much of the fundamental mathematics

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Overview

Time-Varying Systems and Computations is a unique book providing a detailed and consistent exposition of a powerful unifying framework (developed by the authors) for the study of time-variant systems and the computational aspects and problems that arise in this context. While complex function theory and linear algebra provide much of the fundamental mathematics needed by engineers engaged in numerical computations, signal processing and/or control, there has long been a large, abstruse gap between the two fields. This book shows the reader how the gap between analysis and linear algebra can be bridged. In a fascinating monograph, the authors explore, discover and exploit many interesting links that exist between classical linear algebraic concepts and complex analysis.
Time-Varying Systems and Computations opens for the reader new and exciting perspectives on linear algebra from the analysis point of view. It clearly explains a framework that allows the extension of classical results, from complex function theory to the case of time-variant operators and even finite-dimensional matrices. These results allow the user to obtain computationally feasible schemes and models for complex and large-scale systems.
Time-Varying Systems and Computations will be of interest to a broad spectrum of researchers and professionals, including applied mathematicians, control theorists, systems theorists and numerical analysts. It can also be used as a graduate course in linear time-varying system theory.

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Product Details

ISBN-13:
9780792381891
Publisher:
Springer US
Publication date:
06/30/1998
Edition description:
1998
Pages:
460
Product dimensions:
9.21(w) x 6.14(h) x 1.06(d)

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Table of Contents

Preface
Acknowledgments
1Introduction1
2Notation and Properties of Non-Uniform Spaces19
3Time-Varying State Space Realizations33
4Diagonal Algebra73
5Operator Realization Theory87
6Isometric and Inner Operators121
7Inner-Outer Factorization and Operator Inversion145
8J-Unitary Operators191
9Algebraic Interpolation233
10Hankel-Norm Model Reduction263
11Low-Rank Matrix Approximation and Subspace Tracking307
12Orthogonal Embedding337
13Spectral Factorization363
14Lossless Cascade Factorizations383
15Conclusion419
Appendices423
A-Hilbert space definitions and properties423
References435
Glossary of notation453
Index455

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