04712nam a22005535i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001700188072002300205082001600228100002500244245015200269264004000421300002900461336002600490337002600516338003600542347002400578490009100602505137900693520135402072650001703426650001903443650001303462650003603475650002103511650002503532650002403557650001703581650002103598650005203619650004503671650003703716700003403753700003203787710003403819773002003853776003603873830009103909856004804000912001404048999001904062952007704081978-3-7643-8753-2DE-He21320180115171801.0cr nn 008mamaa110128s2010 sz | s |||| 0|eng d a97837643875329978-3-7643-8753-27 a10.1007/978-3-7643-8753-22doi 4aQA329-329.9 7aPBKF2bicssc 7aMAT0370002bisacsh04a515.7242231 aBart, Harm.eauthor.12aA State Space Approach to Canonical Factorization with Applicationsh[electronic resource] /cby Harm Bart, Marinus A. Kaashoek, André C. M. Ran. 1aBasel :bBirkhäuser Basel,c2010. a432 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aOperator Theory: Advances and Applications, Linear Operators and Linear Systems ;v2000 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. aThe 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. 0aMathematics. 0aMatrix theory. 0aAlgebra. 0aFunctions of complex variables. 0aOperator theory. 0aOperations research. 0aManagement science.14aMathematics.24aOperator Theory.24aLinear and Multilinear Algebras, Matrix Theory.24aOperations Research, Management Science.24aFunctions of a Complex Variable.1 aKaashoek, Marinus A.eauthor.1 aRan, André C. M.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783764387525 0aOperator Theory: Advances and Applications, Linear Operators and Linear Systems ;v20040uhttp://dx.doi.org/10.1007/978-3-7643-8753-2 aZDB-2-SMA c373006d373006 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK