Książki

The present book deals with canonical factorization of matrix and operator functions that appear in state space form or that can be transformed into such a form. A unified geometric approach is used. The main results are all expressed explicitly in terms of matrices or operators, which are parameters of the state space representation. The applications concern different classes of convolution equations. A large part the book deals with rational matrix functions only.

A State Space Approach to Canonical Factorization with Applications

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.