Developments in Mathematics

Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control

Authors: Johnson, R., Obaya, R., Novo, S., Núñez, C., Fabbri, R.

  • Provides a detailed study of the concept of rotation and of the solutions of linear nonautonomous Hamiltonian systems of general dimension
  • Explores the applications of linear Hamiltonian systems to questions arising in classical oscillation theory of such systems, and to the theory of linear control systems with time-varying coefficients
  • Applies known results of the theory of periodic Hamiltonian systems to the general nonautonomous case and presents various new properties
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eBook 91,62 €
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  • ISBN 978-3-319-29025-6
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  • Immediate eBook download after purchase
Hardcover 114,39 €
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  • ISBN 978-3-319-29023-2
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  • Usually dispatched within 3 to 5 business days.
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About this book

This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations.
The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense.
The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory.

Table of contents (8 chapters)

  • Nonautonomous Linear Hamiltonian Systems

    Johnson, Russell (et al.)

    Pages 1-75

    Preview Buy Chapter 30,19 €
  • The Rotation Number and the Lyapunov Index for Real Nonautonomous Linear Hamiltonian Systems

    Johnson, Russell (et al.)

    Pages 77-124

    Preview Buy Chapter 30,19 €
  • The Floquet Coefficient for Nonautonomous Linear Hamiltonian Systems: Atkinson Problems

    Johnson, Russell (et al.)

    Pages 125-179

    Preview Buy Chapter 30,19 €
  • The Weyl Functions

    Johnson, Russell (et al.)

    Pages 181-248

    Preview Buy Chapter 30,19 €
  • Weak Disconjugacy for Linear Hamiltonian Systems

    Johnson, Russell (et al.)

    Pages 249-328

    Preview Buy Chapter 30,19 €

Buy this book

eBook 91,62 €
price for Spain (gross)
  • ISBN 978-3-319-29025-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-319-29023-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control
Authors
Series Title
Developments in Mathematics
Series Volume
36
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-29025-6
DOI
10.1007/978-3-319-29025-6
Hardcover ISBN
978-3-319-29023-2
Series ISSN
1389-2177
Edition Number
1
Number of Pages
XXI, 497
Topics