Time-Variant and Quasi-separable Systems

Matrix Theory, Recursions and Computations

Inbunden, Engelska, 2024

Av Patrick Dewilde, Klaus Diepold, Alle-Jan Van der Veen, Patrick (Technische Universitat Munchen) Dewilde, Klaus (Technische Universitat Munchen) Diepold, The Netherlands) Van der Veen, Alle-Jan (Technische Universiteit Delft, Alle-Jan Van Der Veen

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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.

Produktinformation

Utgivningsdatum2024-10-31
Mått177 x 250 x 23 mm
Vikt735 g
FormatInbunden
SpråkEngelska
Antal sidor330
FörlagCambridge University Press
ISBN9781009455626

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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.

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.