Overview
- Presents a systematic study that develops the functional model approach for multivariable linear systems.
- Provide a bridge between classical frequency response techniques and state space approaches, thereby providing a unified algebraic approach to systems with different kind of system representations.
- Contains many examples, exercises and notes and references that complement the main text. Book should thus be suitable for self-study, as well as courses and seminars.
Part of the book series: Universitext (UTX)
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Table of contents (12 chapters)
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Front Matter
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Algebraic Systems Theory: Foundations
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Front Matter
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Algebraic Systems Theory: Advanced Topics
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Front Matter
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Networks of Linear Systems
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Front Matter
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Back Matter
Keywords
About this book
This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as well as feedback control and observer theory. The potential of networks for linear systems in controlling large-scale networks of interconnected dynamical systems could provide insight into a diversity of scientific and technological disciplines. The scope of the book is quite extensive, ranging from introductory material to advanced topics of current research, making it a suitable reference for graduate students and researchers in the field of networks of linear systems. Part I can be used as the basis for a first course in Algebraic System Theory, while Part II serves for a second, advanced, course on linear systems.
Finally, Part III, which is largely independent of the previous parts, is ideally suited for advanced research seminars aimed at preparing graduate students for independent research. “Mathematics of Networks of Linear Systems” contains a large number of exercises and examples throughout the text making it suitable for graduate courses in the area.
Reviews
“In the voluminous book under review the authors illustrate their perspective on modelling and control of networks of linear finite-dimensional systems. … This is an excellent book that can be appreciated both by readers familiar with the polynomial approach, and by readers unaccustomed to functional models. … The historical sections at the end of each chapter are helpful because they explain the broader context and suggest further reading to both types of readers.” (Paolo Rapisarda, Mathematical Reviews, March, 2016)
Authors and Affiliations
About the authors
Paul A. Fuhrmann is Professor Emeritus in the Department of Mathematics at Ben-Gurion University of the Negev. His current research interests are in the following directions: Algebraic System Theory, control, observation and model reduction for networks of linear systems.
Uwe Helmke is Professor and Chair in Dynamical Systems and Control Theory at the University of Wuerzburg. His current research interests include Algebraic and Differential-Geometric Methods in Control, Linear Systems Theory, Optimization on Manifolds, Formation Control.
Bibliographic Information
Book Title: The Mathematics of Networks of Linear Systems
Authors: Paul A. Fuhrmann, Uwe Helmke
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-16646-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-16645-2Published: 11 June 2015
eBook ISBN: 978-3-319-16646-9Published: 26 May 2015
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIV, 662
Number of Illustrations: 53 b/w illustrations
Topics: Linear and Multilinear Algebras, Matrix Theory, Systems Theory, Control, Control and Systems Theory
Industry Sectors: IT & Software