The Mathematics of Networks of Linear Systems

  • Paul A. Fuhrmann
  • Uwe Helmke

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Paul A. Fuhrmann, Uwe Helmke
    Pages 1-20
  3. Algebraic Systems Theory: Foundations

    1. Front Matter
      Pages 21-21
    2. Paul A. Fuhrmann, Uwe Helmke
      Pages 23-83
    3. Paul A. Fuhrmann, Uwe Helmke
      Pages 85-140
    4. Paul A. Fuhrmann, Uwe Helmke
      Pages 141-206
  4. Algebraic Systems Theory: Advanced Topics

    1. Front Matter
      Pages 207-207
    2. Paul A. Fuhrmann, Uwe Helmke
      Pages 209-279
    3. Paul A. Fuhrmann, Uwe Helmke
      Pages 281-353
    4. Paul A. Fuhrmann, Uwe Helmke
      Pages 355-408
  5. Networks of Linear Systems

    1. Front Matter
      Pages 409-409
    2. Paul A. Fuhrmann, Uwe Helmke
      Pages 411-466
    3. Paul A. Fuhrmann, Uwe Helmke
      Pages 467-505
    4. Paul A. Fuhrmann, Uwe Helmke
      Pages 507-552
    5. Paul A. Fuhrmann, Uwe Helmke
      Pages 553-600
    6. Paul A. Fuhrmann, Uwe Helmke
      Pages 601-644
  6. Back Matter
    Pages 645-662

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.


Algebraic Systems Theory Control Engineering Cyber-Physical Systems Functional Models and Shift Spaces Graph Theory Interconnected Dynamical Systems Linear Systems Network Science Synchronization

Authors and affiliations

  • Paul A. Fuhrmann
    • 1
  • Uwe Helmke
    • 2
  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.Universität Würzburg, Institute of MathematicsWürzburgGermany

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-16645-2
  • Online ISBN 978-3-319-16646-9
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking
IT & Software
Consumer Packaged Goods
Energy, Utilities & Environment