Bart / Gohberg / Kaashoek Factorization of Matrix and Operator Functions: The State Space Method

1. Auflage 2007
ISBN: 978-3-7643-8268-1
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 412 Seiten

This book delineates the various types of factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, and the theory of job scheduling in operations research. The book presents a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions.

Autoren/Hrsg.

Bart, Harm

Gohberg, Israel

Kaashoek, Marinus

Inhaltsverzeichnis

1;Contents;7
2;Preface;11
3;Introduction;13
4;Motivating Problems, Systems and Realizations;16
5;Motivating Problems;17
6;Operator Nodes, Systems, and Operations on Systems;34
7;Various Classes of Systems;58
8;Realization and Linearization of Operator Functions;74
9;Factorization and Riccati Equations;86
10;Canonical Factorization and Applications;98
11;Minimal Realization and Minimal Factorization;111
12;Minimal Systems;112
13;Minimal Realizations and Pole-Zero Structure;136
14;Minimal Factorization of Rational Matrix Functions;169
15;Degree One Factors, Companion Based Rational Matrix Functions, and Job Scheduling;186
16;Factorization into Degree One Factors;187
17;Complete Factorization of Companion Based Matrix Functions;215
18;Quasicomplete Factorization and Job Scheduling;271
19;Stability of Factorization and of Invariant Subspaces;320
20;Stability of Spectral Divisors;321
21;Stability of Divisors;341
22;Factorization of Real Matrix Functions;376
23;Bibliography;393
24;List of Symbols;401
25;Index;405