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 -