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).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2010 Birkhäuser/Springer Basel AG
About this chapter
Cite this chapter
Bart, H., Kaashoek, M.A., Ran, A.C.M. (2010). Canonical factorization and Riccati equations. In: A State Space Approach to Canonical Factorization with Applications. Operator Theory: Advances and Applications, vol 200. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8753-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8753-2_13
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8752-5
Online ISBN: 978-3-7643-8753-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)