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:
    non sort: A
    title: State Space Approach to Canonical Factorization with Applications
  name:
    name part: Bart, Harm.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Kaashoek, Marinus A.
    role:
      role term: author.
  name:
    name part: Ran, André C. M.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2010
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: 432 p. online resource.
  abstract: The present book deals with canonical factorization problems for di?erent classes of matrix and operator functions. Such problems appear in various areas of ma- ematics and its applications. The functions we consider havein common that they appear in the state space form or can be represented in such a form. The main results are all expressed in terms of the matrices or operators appearing in the state space representation. This includes necessary and su?cient conditions for canonical factorizations to exist and explicit formulas for the corresponding f- tors. Also, in the applications the entries in the state space representation play a crucial role. Thetheorydevelopedinthebookisbasedonageometricapproachwhichhas its origins in di?erent ?elds. One of the initial steps can be found in mathematical systems theory and electrical network theory, where a cascade decomposition of an input-output system or a network is related to a factorization of the associated transfer function. Canonical factorization has a long and interesting history which starts in the theory of convolution equations. Solving Wiener-Hopf integral equations is closely related to canonical factorization. The problem of canonical factorization also appears in other branches of applied analysis and in mathematical systems theory, in H -control theory in particular.
  table of contents: Convolution equations, canonical factorization and the state space method -- The role of canonical factorization in solving convolution equations -- The state space method and factorization -- Convolution equations with rational matrix symbols -- Explicit solutions using realizations -- Factorization of non-proper rational matrix functions -- Equations with non-rational symbols -- Factorization of matrix functions analytic in a strip -- Convolution equations and the transport equation -- Wiener-Hopf factorization and factorization indices -- Factorization of selfadjoint rational matrix functions -- Preliminaries concerning minimal factorization -- Factorization of positive definite rational matrix functions -- Pseudo-spectral factorizations of selfadjoint rational matrix functions -- Review of the theory of matrices in indefinite inner product spaces -- Riccati equations and factorization -- Canonical factorization and Riccati equations -- The symmetric algebraic Riccati equation -- J-spectral factorization -- Factorizations and symmetries -- Factorization of positive real rational matrix functions -- Contractive rational matrix functions -- J-unitary rational matrix functions -- Applications of J-spectral factorizations -- Application to the rational Nehari problem -- Review of some control theory for linear systems -- H-infinity control applications.
  note: by Harm Bart, Marinus A. Kaashoek, André C. M. Ran.
  subject:
    topic: Mathematics
  subject:
    topic: Matrix theory
  subject:
    topic: Algebra
  subject:
    topic: Functions of complex variables
  subject:
    topic: Operator theory
  subject:
    topic: Operations research
  subject:
    topic: Management science
  subject:
    topic: Mathematics
  subject:
    topic: Operator Theory
  subject:
    topic: Linear and Multilinear Algebras, Matrix Theory
  subject:
    topic: Operations Research, Management Science
  subject:
    topic: Functions of a Complex Variable
  classification: QA329-329.9
  classification: 515.724
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Operator Theory: Advances and Applications, Linear Operators and Linear Systems ; 200
  identifier: 9783764387532
  identifier: http://dx.doi.org/10.1007/978-3-7643-8753-2
  record info:
    record creation date: 110128
    record change date: 20151204152454.0
    record identifier: 978-3-7643-8753-2