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Linear State/Signal Systems

£150.00

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: May 2022
  • availability: Available
  • format: Hardback
  • isbn: 9781316519677

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About the Authors
  • The authors explain in this work a new approach to observing and controlling linear systems whose inputs and outputs are not fixed in advance. They cover a class of linear time-invariant state/signal system that is general enough to include most of the standard classes of linear time-invariant dynamical systems, but simple enough that it is easy to understand the fundamental principles. They begin by explaining the basic theory of finite-dimensional and bounded systems in a way suitable for graduate courses in systems theory and control. They then proceed to the more advanced infinite-dimensional setting, opening up new ways for researchers to study distributed parameter systems, including linear port-Hamiltonian systems and boundary triplets. They include the general non-passive part of the theory in continuous and discrete time, and provide a short introduction to the passive situation. Numerous examples from circuit theory are used to illustrate the theory.

    • Written by leading experts in the field, incorporating years of research
    • Includes over 60 worked examples to illustrate the theory
    • Contains a number of new results for linear time-invariant input/state/output systems
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    Product details

    • Date Published: May 2022
    • format: Hardback
    • isbn: 9781316519677
    • length: 1080 pages
    • dimensions: 251 x 174 x 61 mm
    • weight: 1.877kg
    • availability: Available
  • Table of Contents

    1. Introduction and overview
    2. State/signal systems: trajectories, transformations, and interconnections
    3. State/signal systems: dynamic and frequency domain properties
    4. Input/state/output representations
    5. Input/state/output systems: dynamic and frequency domain properties
    6. Bounded input/state/output systems in continuous and discrete time
    7. Bounded state/signal systems in continuous and discrete time
    8. Semi-bounded input/state/output systems
    9. Semi-bounded state/signal systems
    10. Resolvable input/state/output and state/signal nodes
    11. Frequency domain input/state/output systems
    12. Frequency domain state/signal systems
    13. Internally well-posed systems
    14. Well-posed input/state/output systems
    15. Well-posed state/signal systems
    Appendix
    Operators and analytic vector bundles in H-spaces
    References
    Index.

  • Authors

    Damir Z. Arov, South Ukrainian Pedagogical University
    Damir Z. Arov is Professor in Mathematics at South-Ukrainian National Pedagogical University in Odessa. He introduced the notion of ε-entropy (predating the Kolmogorov–Sinai entropy), is one of the authors behind the Adamyan–Arov–Krein theory used in H∞ control, and developed passive systems theory and the theory of J-contractive matrix-valued functions. He has written approximately 200 journal articles and co-authored three monographs with Professor Harry Dym. Professor Arov, is an honorary doctor from Åbo Akademi University, Finland, and has received the Krein prize from the Ukrainian Academy of Sciences.

    Olof J. Staffans, Åbo Akademi University, Finland
    Olof J. Staffans is Professor Emeritus in Mathematics at Åbo Akademi University in Finland. He is the author of Well-Posed Linear Systems (Cambridge, 2005) and a co-author of Volterra Integral and Functional Equations (Cambridge, 1990), and has published more than 100 journal articles. He is a fellow of the American Mathematical Society and a member of the Finnish Society of Sciences and Letters from which he received the E. J. Nyström award.

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