A State Space Approach to Canonical Factorization with Applications

Abstract

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.