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Linear Operators and Linear Systems
An Analytical Approach to Control Theory

Part of London Mathematical Society Student Texts

  • Date Published: July 2004
  • availability: Available
  • format: Paperback
  • isbn: 9780521546195

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  • Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes material on pure mathematical topics such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view. Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engineering.

    • Presents the common ground between linear operators and linear systems in an elementary style
    • Includes recent material on power signal spaces and delay systems that is not available in other books
    • Of wide interest - pure mathematicians, applied mathematicians and engineers simultaneously
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    Reviews & endorsements

    'The author has succeeded in covering a large amount of material in rather few pages. this volume gives a good introduction to the theory of infinite-dimensional systems, although mostly for those described by delay differential equations (rather than partial differential equations). It also contains much material that should be of interest to engineers and mathematicians. there are numerous examples and exercises, ranging from concrete to abstract, which contribute to delineate the natural limits of some of the results.' Zentralblatt MATH

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    Product details

    • Date Published: July 2004
    • format: Paperback
    • isbn: 9780521546195
    • length: 178 pages
    • dimensions: 229 x 160 x 11 mm
    • weight: 0.32kg
    • contains: 6 b/w illus. 101 exercises
    • availability: Available
  • Table of Contents

    1. Operators and Hardy spaces
    2. Closed operators
    3. Shift-invariance and causality
    4. Stability and stabilization
    5. Spaces of persistent signals
    6. Delay systems.

  • Resources for

    Linear Operators and Linear Systems

    Jonathan R. Partington

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  • Author

    Jonathan R. Partington, University of Leeds
    Jonathan R. Partington is a Professor of Applied Functional Analysis at Leeds University. He has served as editor of Journal of the London Mathematical Society and is coordinator of Leeds node in European Research Training network in Analysis and Operators. Author of some 100 papers in mathematics and engineering, he is also the author of An Introduction to Hankel Operators and Interpolation, Identification and Sampling.

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