A State Space Approach to Canonical Factorization with Applications
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Beschreibung
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.
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
Autor*in
Harm Bart
Themen in »A State Space Approach to Canonical Factorization with Applications«
Matrix algebra convolution factorization matrix function state space matrix theory
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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)()