The state space method and factorization

Abstract

This chapter describes in detail the elements of the state space method that are used throughout this book. The central notion is that of a realization of a matrix or operator function. The chapter consists of six sections. Section 2.1 presents preliminaries on realization, including the relevant definitions and the connection with systems theory. In the next two sections the realization problem is discussed. First for rational matrix functions in Section 2.2, and then for analytic operator functions in a possibly infinite dimensional setting in Section 2.3. The last three sections are devoted to the main operations on realizations that are needed in this book: inversion (Section 2.4), taking products (Section 2.5), and factorization (Section 2.6).