Factorization of Matrix and Operator Functions: The State Space Method

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...

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Bibliographic Details
Main Authors: Bart, Harm, Gohberg, Israel (Author), Kaashoek, Marinus A. (Author), Ran, André C.M. (Author)
Format: eBook
Published: Basel Birkhäuser 2008, 2008
Edition:1st ed. 2008
Series:Linear Operators and Linear Systems
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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