Operator Theory: Advances and Applications

A State Space Approach to Canonical Factorization with Applications

Authors: Bart, H., Gohberg, I., Kaashoek, M.A., Ran, A.

  • The state space factorization method is systematically used and developed further for various classes of matrix and operator functions
  • Places emphasis on canonical factorization problems, including spectral and J-spectral factorizations problems and related Ricatti equations
  • Covers elements of H-infinity control theory and the related Nehari approximation problem
  • A large part the book deals with rational matrix functions only
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About this book

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.

Reviews

From the reviews:

“This monograph develops a theory of canonical factorizations for various classes of matrix and operator functions, where the functions are represented in the form of a transfer function of an input-state-output linear system. … The book is self-contained and accessible for specialists in different areas of mathematics, science, and engineering.” (Dmitry Kaliuzhnyi-Verbovetskyi, Zentralblatt MATH, Vol. 1203, 2011)

Table of contents (21 chapters)

  • Introduction

    Bart, Harm (et al.)

    Pages 1-6

  • The role of canonical factorization in solving convolution equations

    Bart, Harm (et al.)

    Pages 9-17

  • The state space method and factorization

    Bart, Harm (et al.)

    Pages 19-33

  • Explicit solutions using realizations

    Bart, Harm (et al.)

    Pages 37-56

  • Factorization of non-proper rational matrix functions

    Bart, Harm (et al.)

    Pages 57-74

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-7643-8753-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-7643-8752-5
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
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Bibliographic Information

Bibliographic Information
Book Title
A State Space Approach to Canonical Factorization with Applications
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
200
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-8753-2
DOI
10.1007/978-3-7643-8753-2
Hardcover ISBN
978-3-7643-8752-5
Series ISSN
0255-0156
Edition Number
1
Number of Pages
432
Topics