A state space approach to canonical factorization with applications 1st Edition by Harm Bart, Israel Gohberg, Marinus Kaashoek, André Ran 376438753X 9783764387532 by Bart H., Gohberg I., Et Al. 9783764387525, 3764387521 instant download after payment.

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Product details:

ISBN 10: 376438753X 

ISBN 13: 9783764387532

Author: Harm Bart; Israel Gohberg; Marinus A. Kaashoek; André C.M. Ran

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.

Table of contents:

Chapter 0 Introduction

Part I: Convolution equations, canonical factorization and the state space method
Chapter 1 The role of canonical factorization in solving convolution equations
Chapter 2 The state space method and factorization

Part II: Convolution equations with rational matrix symbols
Chapter 3 Explicit solutions using realizations
Chapter 4 Factorization of non-proper rational matrix functions

Part III: Equations with non-rational symbols
Chapter 5 Factorization of matrix functions analytic in a strip
Chapter 6 Convolution equations and the transport equation
Chapter 7 Wiener-Hopf factorization and factorization indices

Part IV: Factorization of selfadjoint rational matrix functions
Chapter 8 Preliminaries concerning minimal factorization
Chapter 9 Factorization of positive definite rational matrix functions
Chapter 10 Pseudo-spectral factorizations of selfadjoint rational matrix functions
Chapter 11 Review of the theory of matrices in indefinite inner product spaces

Part V: Riccati equations and factorization
Chapter 12 Canonical factorization and Riccati equations
Chapter 13 The symmetric algebraic Riccati equation
Chapter 14 J-spectral factorization

Part VI: Factorizations and symmetries
Chapter 15 Factorization of positive real rational matrix functions
Chapter 16 Contractive rational matrix functions
Chapter 17 J-unitary rational matrix functions

Part VII: Applications of J-spectral factorizations
Chapter 18 Application to the rational Nehari problem
Chapter 19 Review of some control theory for linear systems
Chapter 20 H-infinity control applications

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