TY - JOUR

T1 - Spectral Factorization of Time-Varying Functions

AU - Anderson, Brian D.O.

AU - Moore, John B.

AU - Loo, Sonny G.

PY - 1969/9

Y1 - 1969/9

N2 - The determination of the state-space equations of a time-varying finite-dimensional linear system with a prescribed output covariance matrix is considered when the system is excited by Gaussian white-noise inputs. It is shown that a symmetric state covariance matrix provides the key link between the state-space equations of a system and the system output covariance matrix. Furthermore, such a matrix satisfies a linear matrix differential equation if the state-space equations of the system are known, and a matrix Riccati equation if the output covariance matrix of the system is given. Existence results are given for the Riccati equation solution, and discussion of asymptotic solutions of the differential equations is also included.

AB - The determination of the state-space equations of a time-varying finite-dimensional linear system with a prescribed output covariance matrix is considered when the system is excited by Gaussian white-noise inputs. It is shown that a symmetric state covariance matrix provides the key link between the state-space equations of a system and the system output covariance matrix. Furthermore, such a matrix satisfies a linear matrix differential equation if the state-space equations of the system are known, and a matrix Riccati equation if the output covariance matrix of the system is given. Existence results are given for the Riccati equation solution, and discussion of asymptotic solutions of the differential equations is also included.

UR - http://www.scopus.com/inward/record.url?scp=35348967742&partnerID=8YFLogxK

U2 - 10.1109/TIT.1969.1054360

DO - 10.1109/TIT.1969.1054360

M3 - Article

AN - SCOPUS:35348967742

SN - 0018-9448

VL - 15

SP - 550

EP - 557

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 5

ER -