Appendix

van Schuppen, J.H.

Appendix

Matrix Equations

Book chapter (2021)

Authors

J.H. van Schuppen Mathematical Physics -

Research Group

Mathematical Physics () (TU Delft)

Lyapunov equation Algebraic Riccati equation

To reference this document use:

http://resolver.tudelft.nl/uuid:6f86fd7f-6dba-4650-b918-dd7373978024

More Info

expand_more

Published Date

2021

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

Abstract

The Lyapunov equation and the algebraic Riccati equation are treated in depth. The Lyapunov equation arises as the equation for the asymptotic covariance matrix of the state of a stationary Gaussian system. The algebraic Riccati equation arises in the Kalman filter, in stochastic control, and in stochastic realization of a Gaussian system. Results for both equations are provided on: the existence of a solution, uniqueness with respect to conditions, a description of the set of all solutions if applicable, particular properties of solutions, and on the computation of solutions.