Overview
- The state space factorization method is systematically used and developed further for various classes of matrix and operator functions
- Emphasis is put on canonical factorization problems, including spectral and J-spectral factorizations problems and related Ricatti equations
- Elements of H-infinity control theory and the related Nehari approximation problem are covered
- Applications concern elements of H-infinity control theory and the related Nehari approximation problem, problems in mathematical analysis (inversion problems for singular integral equations and Wiener-Hopf integral equations, related Riemann Hilbert problems), and problems from mathematical physics (linear transport theory)
- A large part the book deals with rational matrix functions only
- Includes supplementary material: sn.pub/extras
Part of the book series: Operator Theory: Advances and Applications (OT, volume 200)
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Table of contents (21 chapters)
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Introduction
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Convolution equations, canonical factorization and the state space method
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Convolution equations with rational matrix symbols
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Equations with non-rational symbols
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Factorization of selfadjoint rational matrix functions
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Riccati equations and factorization
Keywords
About this book
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)Authors and Affiliations
Bibliographic Information
Book Title: A State Space Approach to Canonical Factorization with Applications
Authors: Harm Bart, Marinus A. Kaashoek, André C. M. Ran
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-7643-8753-2
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2010
Hardcover ISBN: 978-3-7643-8752-5Published: 15 April 2010
eBook ISBN: 978-3-7643-8753-2Published: 09 February 2011
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: 432
Topics: Operator Theory, Linear and Multilinear Algebras, Matrix Theory, Operations Research, Management Science, Functions of a Complex Variable