Time-Variant and Quasi-separable Systems
Matrix Theory, Recursions and Computations
Published on 31. October 2024
Book
Hardback
330 pages
978-1-009-45562-6 (ISBN)
Description
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.
Reviews / Votes
'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 TechnologyMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Illustrations
Worked examples or Exercises
Dimensions
Height: 250 mm
Width: 175 mm
Thickness: 22 mm
Weight
754 gr
ISBN-13
978-1-009-45562-6 (9781009455626)
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Schweitzer Classification
Persons
Patrick Dewilde was a professor at the Delft University of Technology for 31 years and previously Director of the Delft Institute for Microelectronics, Chairman of a major Dutch research funding agency and Director of the Institute of Advanced Study of the Technical University of Munich. He is an Institute of Electrical and Electronics Engineers (IEEE) Fellow, a winner of the IEEE Belevitch Award and an elected member of the Dutch Royal Academy of Arts and Science. Klaus Diepold is a professor at the Technical University of Munich. During his time in industry, he was the chief architect of award-winning software tools MotionPerfect and SteadyHand and is a coauthor of 'Understanding MPEG-4: Technology and Business Insights' (2004). He is a board member of the Center for Digital Technology and Management and Fellow for Innovation in University Education. He was awarded the Start-Up Mentor of Excellence Award in 2021 by the Technical University of Munich. In 2023 he received the Unipreneurs Award by the Federal Ministry for Education and Research for his entrepreneurial activities. Alle-Jan Van der Veen is Professor and Chair of the Signals and Systems group at Delft University of Technology. He is an IEEE Fellow and IEEE SPS Vice President - Technical Directions. Previous IEEE positions include: Editor-in-Chief of 'Transactions on Signal Processing,' Chairman of the Signal Processing Society, elected member of the SPS Board of Governors and Chair of the SPS Signal Processing Theory and Methods Technical Committee and the Kilby Medal selection committee.
Content
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.