A State Space Approach to Canonical Factorization with Applications

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 suc...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Bart, Harm (Author), Gohberg, Israel (Author), Kaashoek, Marinus A. (Author), Ran, André C.M (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2010.
Edition:1st ed. 2010.
Series:Operator Theory: Advances and Applications, 200
Subjects:
Operator theory.
Algebras, Linear.
Operations research.
Management science.
Functions of complex variables.
Operator Theory.
Linear Algebra.
Operations Research, Management Science .
Functions of a Complex Variable.
Online Access:Texto Completo
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.

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