Time-Variant and Quasi-separable Systems
Time-Variant and Quasi-separable Systems
Klaus Diepold, Technische Universität München
Alle-Jan Van der Veen, Technische Universiteit Delft, The Netherlands
Matrix theory is the lingua franca of everyone who deals with dynamically evolving systems, and familiarity with efficient matrix computations is an essential part of the modern curriculum in dynamical systems and associated computation. This is a master's-level textbook on dynamical systems and computational matrix algebra. It is based on the remarkable identity of these two disciplines in the context of linear, time-variant, discrete-time systems and their algebraic equivalent, quasi-separable systems. The authors' approach provides a single, transparent framework that yields simple derivations of basic notions, as well as new and fundamental results such as constrained model reduction, matrix interpolation theory and scattering theory. This book outlines all the fundamental concepts that allow readers to develop the resulting recursive computational schemes needed to solve practical problems. An ideal treatment for graduate students and academics in electrical and computer engineering, computer science and applied mathematics.
- The new method adheres to classical system- and matrix-theory traditions but applies them in a transparent and appealing way
- Focuses on elementary matrix algebra and presents this in the most effective way
- Connects linear dynamical systems and matrix algebra to allow readers to explore the methods using available software tools
Reviews & endorsements
'This book represents the first comprehensive single-volume coverage on signal processing, dynamical systems and numerical algorithms. It will be a timely reference for students, practitioners, and researchers in the areas of systems, control, estimation, identification, optimization and modern data sciences - since math is the cornerstone of AI. Sun-Yuan Kung, Princeton University
'Finally techniques that deserve to be widely known are presented in a highly accessible manner, by the pioneers of the field. A must-read for anyone interested in structured-matrix computations, systems theory, or signal processing.' Shivkumar Chandrasekaran, University of California, Santa Barbara
'This book, by renowned experts in the related fields of dynamical systems, numerical linear algebra and signal processing, offers an excellent and comprehensive treatment of dynamical systems and computational matrix algebra, presenting clearly explained foundational concepts in Part I alongside innovative techniques in Part II. Perfect for graduate students and academics in electrical and computer engineering, computer science, and applied mathematics, it equips readers with essential knowledge to develop robust computational schemes for solving real-world problems effectively.' Wil Schilders, TU Eindhoven and TU Munich- IAS
'The topic outlined in this book is of great practical importance consolidated in one volume by outstanding researchers in the field. The great relevance is that it translates theoretical concepts into practical matrix concepts that allow reliable implementations. It is in one word a great reference material for those who want to make substantial contributions in the field of time varying systems!' Michel Verhaegen, Delft University of Technology
'The book develops a connection between linear dynamical systems and computer executed matrix calculus to understand the behavior of a dynamical system as well as efficient computations. It gives, in a unique and novel way, a unified presentation of the crucial results in modern systems theory, scattering theory, and (Schur-type) parametrization/interpolation. The book offers a systematic but also fully didactical introduction to the unified theory of nest algebras on mathematical side, time-variant systems on system theory, and semi-separable systems on the numerical side.' Jan Zarzycki, Wroclaw University of Science and Technology
Product details
No date availableAdobe eBook Reader
9781009455664
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Table of Contents
- Part I. Lectures on Basics, with Examples:
- 1. A first example: optimal quadratic control
- 2. Dynamical systems
- 3. LTV (quasi-separable) systems
- 4. System identification
- 5. State equivalence, state reduction
- 6. Elementary operations
- 7. Inner operators and external factorizations
- 8. Inner-outer factorization
- 9. The Kalman filter as an application
- 10. Polynomial representations
- 11. Quasi-separable Moore– Penrose inversion
- Part II. Further Contributions to Matrix Theory:
- 12. LU (spectral) factorization
- 13. Matrix Schur interpolation
- 14. The scattering picture
- 15. Constrained interpolation
- 16. Constrained model reduction
- 17. Isometric embedding for causal contractions
- Appendix. Data model and implementations
- References
- Index.
