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Birkhäuser - Birkhäuser Mathematics | A State Space Approach to Canonical Factorization with Applications

A State Space Approach to Canonical Factorization with Applications

Bart, H., Gohberg, I., Kaashoek, M., Ran, A.C.M.

2010, 432p.

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  • 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

The present book deals with canonical factorization of matrix and operator functions that appear in state space form or that can be transformed into such a form. A unified geometric approach is used. The main results are all expressed explicitly in terms of matrices or operators, which are parameters of the state space representation. The applications concern different classes of convolution equations. The analysis of canonical factorization for functions with symmetries, including spectral and J-spectral factorizations, related Ricatti equations, and elements of H-infinity control theory are also main topics.

This is the second book written by the four authors in which the state space factorization method is systematically used and developed further. In their first book, released in 2007, the emphasis is on non-canonical factorizations and degree one factorizations, in particular. The present book concentrates on canonical factorization and its applications. Together both books present a rich and far reaching update of the 1979 monograph, the first book in the OTAA series, written by the first three authors.

Content Level » Research

Keywords » Matrix - algebra - convolution - factorization - matrix function - state space

Related subjects » Birkhäuser Applied Probability and Statistics - Birkhäuser Mathematics

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