Time-Varying Systems and Computations (Hardcover)

Patrick DeWilde

ISBN 10: 0792381890 / ISBN 13: 9780792381891

Editore: Kluwer Academic Publishers, Dordrecht, 1998

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Hardcover. This text provides a detailed exposition of a 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 this monograph, the authors explore, discover and exploit many links that exist between classical linear algebraic concepts and complex analysis. The text attempts to open up perspectives on linear algebra from the analysis point of view. It 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.The volume should 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. Complex function theory and linear algebra provide much of the basic mathematics needed by engineers engaged in numerical computations, signal processing or control. The transfer function of a linear time invariant system is a function of the complex vari able s or z and it is analytic in a large part of the complex plane. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Codice articolo 9780792381891

Dati bibliografici

• Titolo: Time-Varying Systems and Computations (Hardcover)
• Editore: Kluwer Academic Publishers, Dordrecht
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0792381890
• ISBN 13: 9780792381891
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

Riassunto

Complex function theory and linear algebra provide much of the basic mathematics needed by engineers engaged in numerical computations, signal processing or control. The transfer function of a linear time invariant system is a function of the complex vari­ able s or z and it is analytic in a large part of the complex plane. Many important prop­ erties of the system for which it is a transfer function are related to its analytic prop­ erties. On the other hand, engineers often encounter small and large matrices which describe (linear) maps between physically important quantities. In both cases similar mathematical and computational problems occur: operators, be they transfer functions or matrices, have to be simplified, approximated, decomposed and realized. Each field has developed theory and techniques to solve the main common problems encountered. Yet, there is a large, mysterious gap between complex function theory and numerical linear algebra. For example, complex function theory has solved the problem to find analytic functions of minimal complexity and minimal supremum norm that approxi­ e. g. , as optimal mate given values at strategic points in the complex plane. They serve approximants for a desired behavior of a system to be designed. No similar approxi­ mation theory for matrices existed until recently, except for the case where the matrix is (very) close to singular.

Contenuti

Preface. 1. Introduction. Part I: Realization. 2. Notation and Properties of Non-Uniform Spaces. 3. Time-Varying State Space Realizations. 4. Diagonal Algebra. 5. Operator Realization Theory. 6. Isometric and Inner Operators. 7. Inner-Outer Factorization and Operator Inversion. Part II: Interpolation and Approximation. 8. J-Unitary Operators. 9. Algebraic Interpolation. 10. Hankel-Norm Model Reduction. 11. Low-Rank Matrix Approximation and Subspace Tracking. Part III: Factorization. 12. Orthogonal Embedding. 13. Spectral Factorization. 14. Lossless Cascade Factorizations. 15. Conclusions. Appendices: A. Hilbert Space Definitions and Properties. References. Glossary of Notation. Index.