Appendix
Matrix Equations
Book Chapter
(2021)
Author(s)
Jan H. van Schuppen (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Research Group
Mathematical Physics
DOI related publication
https://doi.org/10.1007/978-3-030-66952-2_22
Final published version
To reference this document use
https://resolver.tudelft.nl/uuid:6f86fd7f-6dba-4650-b918-dd7373978024
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Publication Year
2021
Language
English
Research Group
Mathematical Physics
Pages (from-to)
839-881
Publisher
Springer
ISBN (electronic)
978-3-030-66952-2
Downloads counter
167
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.