Canonical factorization and Riccati equations

Abstract

In this chapter the canonical factorization theorem from Section 7.1 is presented in a different way using the notion of an angular subspace and Riccati equations. In this case one has to look for solutions of the Riccati equation that have additional spectral properties. Section 12.1, which has a preliminary character, deals with angular subspaces, and in particular those that are also spectral subspaces. Section 12.2 deals with the connection between factorization and Riccati equations in general, while Section 12.3 contains the main result. It specifies further the main theorem of the second section for the case of canonical factorization. In Section 12.4, as an application, we solve in state space form the problem of obtaining a right canonical factorization when a left one is given (or reversely).