Sinossi
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. A large part the book deals with rational matrix functions only.
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Recensione
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)Contenuti
Convolution 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.
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A State Space Approach to Canonical Factorization with Applications.
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Basel, Birkhäuser., 2010
ISBN 10: 3764387521
ISBN 13: 9783764387525
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xii, 423p. Hardcover. Versand aus Deutschland / We dispatch from Germany via Air Mail. Einband bestoßen, daher Mängelexemplar gestempelt, sonst sehr guter Zustand. Imperfect copy due to slightly bumped cover, apart from this in very good condition. Stamped. Stamped. Operator Theory Advances and Applications Vol. 200. Sprache: Englisch. Codice articolo 5374GB
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A State Space Approach to Canonical Factorization with Applications (Operator Theory: Advances and Applications, 200)
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A State Space Approach to Canonical Factorization with Applications (Operator Theory: Advances and Applications, 200)
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A State Space Approach to Canonical Factorization with Applications
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Springer, Basel, Birkhäuser Basel, Birkhäuser Apr 2010, 2010
ISBN 10: 3764387521
ISBN 13: 9783764387525
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 432 pp. Englisch. Codice articolo 9783764387525
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The state space factorization method is systematically used and developed further for various classes of matrix and operator functionsEmphasis is put on canonical factorization problems, including spectral and J-spectral factorizations problems an. Codice articolo 5279932
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State Space Approach to Canonical Factorization with Applications
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Condizione: New. This book uses a unified geometric approach to canonical factorization of matrix and operator functions that appear in state space form or that can be transformed into such a form. Results are expressed in terms of matrices or operators. Series: Operator Theory: Advances and Applications. Num Pages: 432 pages, biography. BIC Classification: PBF. Category: (UP) Postgraduate, Research & Scholarly. Dimension: 235 x 155 x 25. Weight in Grams: 818. . 2008. Hardback. . . . . Codice articolo V9783764387525
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Buch. Condizione: Neu. A State Space Approach to Canonical Factorization with Applications | Harm Bart (u. a.) | Buch | 432 S. | Englisch | 2010 | Birkhäuser | EAN 9783764387525 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Codice articolo 101885634
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ISBN 10: 3764387521
ISBN 13: 9783764387525
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Buch. Condizione: Neu. Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 440 pp. Englisch. Codice articolo 9783764387525
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9783764387525
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