rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control
  name:
    name part: Johnson, Russell.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Obaya, Rafael.
    role:
      role term: author.
  name:
    name part: Novo, Sylvia.
    role:
      role term: author.
  name:
    name part: Núñez, Carmen.
    role:
      role term: author.
  name:
    name part: Fabbri, Roberta.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    edition: 1st ed. 2016.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXI, 497 p. online resource.
  abstract: 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: Nonautonomous linear Hamiltonian systems -- The rotation number and the Lyapunov index for real nonautonomous linear Hamiltonian systems -- The Floquet coeffcient for nonautonomous linear Hamiltonian systems: Atkinson problems -- The Weyl functions -- Weak disconjugacy for linear Hamiltonian systems -- Nonautonomous control theory. Linear regulator problem and the Kalman-Bucy filter -- Nonautonomous control theory. A general version of the Yakubovich Frequency Theorem -- Nonautonomous control theory. Linear-quadratic dissipative control processes -- Index -- References.
  note: by Russell Johnson, Rafael Obaya, Sylvia Novo, Carmen Núñez, Roberta Fabbri.
  subject:
    topic: Mathematics
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Differential equations
  subject:
    topic: System theory
  subject:
    topic: Mathematics
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Ordinary Differential Equations
  subject:
    topic: Systems Theory, Control
  classification: QA313
  classification: 515.39
  classification: 515.48
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Developments in Mathematics, 36
  identifier: 9783319290256
  identifier: http://dx.doi.org/10.1007/978-3-319-29025-6
  record info:
    record creation date: 160325
    record change date: 20160325131249.0
    record identifier: 978-3-319-29025-6