A State Space Approach to Canonical Factorization with Applications

• Κύριοι συγγραφείς: Bart, Harm (Συγγραφέας), Kaashoek, Marinus A. (Συγγραφέας), Ran, André C. M. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Birkhäuser Basel, 2010.
• Σειρά: Operator Theory: Advances and Applications, Linear Operators and Linear Systems ; 200
• Θέματα: Mathematics.; Matrix theory.; Algebra.; Functions of complex variables.; Operator theory.; Operations research.; Management science.; Operator Theory.; Linear and Multilinear Algebras, Matrix Theory.; Operations Research, Management Science.; Functions of a Complex Variable.

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 suc...

Πίνακας περιεχομένων:

• Convolution equations, canonical factorization and the state space method
• The role of canonical factorization in solving convolution equations
• The state space method and factorization
• Convolution equations with rational matrix symbols
• Explicit solutions using realizations
• Factorization of non-proper rational matrix functions
• Equations with non-rational symbols
• Factorization of matrix functions analytic in a strip
• Convolution equations and the transport equation
• Wiener-Hopf factorization and factorization indices
• Factorization of selfadjoint rational matrix functions
• Preliminaries concerning minimal factorization
• Factorization of positive definite rational matrix functions
• Pseudo-spectral factorizations of selfadjoint rational matrix functions
• Review of the theory of matrices in indefinite inner product spaces
• Riccati equations and factorization
• Canonical factorization and Riccati equations
• The symmetric algebraic Riccati equation
• J-spectral factorization
• Factorizations and symmetries
• Factorization of positive real rational matrix functions
• Contractive rational matrix functions
• J-unitary rational matrix functions
• Applications of J-spectral factorizations
• Application to the rational Nehari problem
• Review of some control theory for linear systems
• H-infinity control applications.