Time-Variant and Quasi-separable Systems
Matrix Theory, Recursions and Computations

Bringing together systems theory, signal processing and numerical computation, this book presents an appealing novel and combined approach.

Patrick Dewilde (Author), Klaus Diepold (Author), Alle-Jan Van der Veen (Author)

9781009455626, Cambridge University Press

Hardback, published 31 October 2024

330 pages
25 x 17.7 x 2.3 cm, 0.735 kg

'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

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.

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.

Subject Areas: Communications engineering / telecommunications [TJK]