Factorization of Matrix and Operator Functions: The State Space Method

• Main Authors: Bart, Harm (Author), Ran, André C. M. (Author), Gohberg, Israel (Author), Kaashoek, Marinus A. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2008.
• Series: Operator Theory: Advances and Applications, Linear Operators and Linear Systems ; 178
• Subjects: Mathematics.; Matrix theory.; Algebra.; Operator theory.; Number theory.; Operator Theory.; Linear and Multilinear Algebras, Matrix Theory.; Number Theory.

The present book deals with 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 co...

Table of Contents:

• Motivating Problems, Systems and Realizations
• Motivating Problems
• Operator Nodes, Systems, and Operations on Systems
• Various Classes of Systems
• Realization and Linearization of Operator Functions
• Factorization and Riccati Equations
• Canonical Factorization and Applications
• Minimal Realization and Minimal Factorization
• Minimal Systems
• Minimal Realizations and Pole-Zero Structure
• Minimal Factorization of Rational Matrix Functions
• Degree One Factors, Companion Based Rational Matrix Functions, and Job Scheduling
• Factorization into Degree One Factors
• Complete Factorization of Companion Based Matrix Functions
• Quasicomplete Factorization and Job Scheduling
• Stability of Factorization and of Invariant Subspaces
• Stability of Spectral Divisors
• Stability of Divisors
• Factorization of Real Matrix Functions.