000 04594nam a22005295i 4500
001 978-3-7643-8753-2
003 DE-He213
005 20140220084552.0
007 cr nn 008mamaa
008 110128s2010 sz | s |||| 0|eng d
020 _a9783764387532
_9978-3-7643-8753-2
024 7 _a10.1007/978-3-7643-8753-2
_2doi
050 4 _aQA329-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.724
_223
100 1 _aBart, Harm.
_eauthor.
245 1 2 _aA State Space Approach to Canonical Factorization with Applications
_h[electronic resource] /
_cby Harm Bart, Marinus A. Kaashoek, André C. M. Ran.
264 1 _aBasel :
_bBirkhäuser Basel,
_c2010.
300 _a432p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aOperator Theory: Advances and Applications, Linear Operators and Linear Systems ;
_v200
505 0 _aConvolution 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.
520 _aThe 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 transport equation, singular integral equations, Wiener-Hopf equations with symbols analytic in a strip, and equations involving factorization of non-proper rational matrix functions. 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 book 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.
650 0 _aMathematics.
650 0 _aMatrix theory.
650 0 _aFunctions of complex variables.
650 0 _aOperator theory.
650 0 _aOperations research.
650 1 4 _aMathematics.
650 2 4 _aOperator Theory.
650 2 4 _aLinear and Multilinear Algebras, Matrix Theory.
650 2 4 _aOperations Research, Mathematical Programming.
650 2 4 _aFunctions of a Complex Variable.
700 1 _aKaashoek, Marinus A.
_eauthor.
700 1 _aRan, André C. M.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783764387525
830 0 _aOperator Theory: Advances and Applications, Linear Operators and Linear Systems ;
_v200
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-7643-8753-2
912 _aZDB-2-SMA
999 _c112984
_d112984