TY - CHAP
T1 - Appendix
T2 - Matrix Equations
AU - van Schuppen, Jan H.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Algebraic Riccati equation
KW - Lyapunov equation
UR - http://www.scopus.com/inward/record.url?scp=85112536499&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-66952-2_22
DO - 10.1007/978-3-030-66952-2_22
M3 - Chapter
AN - SCOPUS:85112536499
T3 - Communications and Control Engineering
SP - 839
EP - 881
BT - Control and System Theory of Discrete-Time Stochastic Systems
PB - Springer
ER -