A Note on a Cross Riccatian and Related Properties for Symmetric Stochastic Realizations

Jose A. Ramos; Erik I. Verriest

doi:10.1109/9.24212

A Note on a Cross Riccatian and Related Properties for Symmetric Stochastic Realizations

Jose A. Ramos
, Erik I. Verriest

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Recent results concerning cross Grammians for both SlSO and symmetric MIMO systems are extended for time-invariant stochastic systems. The extension is based on a cross Riccatian matrix and several results from stochastic realization theory. It is shown that the cross Riccatian can be obtained from the solution to a cross Riccati equation carrying properties from both a forward and a backwards innovations representation. Other symmetry properties similar to those of the cross Grammian are introduced, along with their connection to balanced stochastic realizations.

Original language	American English
Journal	IEEE Transactions on Automatic Control
Volume	34
DOIs	https://doi.org/10.1109/9.24212
State	Published - May 1 1989

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Computer Sciences

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title = "A Note on a Cross Riccatian and Related Properties for Symmetric Stochastic Realizations",

abstract = " Recent results concerning cross Grammians for both SlSO and symmetric MIMO systems are extended for time-invariant stochastic systems. The extension is based on a cross Riccatian matrix and several results from stochastic realization theory. It is shown that the cross Riccatian can be obtained from the solution to a cross Riccati equation carrying properties from both a forward and a backwards innovations representation. Other symmetry properties similar to those of the cross Grammian are introduced, along with their connection to balanced stochastic realizations.",

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journal = "IEEE Transactions on Automatic Control",

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AU - Ramos, Jose A.

AU - Verriest, Erik I.

PY - 1989/5/1

Y1 - 1989/5/1

N2 - Recent results concerning cross Grammians for both SlSO and symmetric MIMO systems are extended for time-invariant stochastic systems. The extension is based on a cross Riccatian matrix and several results from stochastic realization theory. It is shown that the cross Riccatian can be obtained from the solution to a cross Riccati equation carrying properties from both a forward and a backwards innovations representation. Other symmetry properties similar to those of the cross Grammian are introduced, along with their connection to balanced stochastic realizations.

AB - Recent results concerning cross Grammians for both SlSO and symmetric MIMO systems are extended for time-invariant stochastic systems. The extension is based on a cross Riccatian matrix and several results from stochastic realization theory. It is shown that the cross Riccatian can be obtained from the solution to a cross Riccati equation carrying properties from both a forward and a backwards innovations representation. Other symmetry properties similar to those of the cross Grammian are introduced, along with their connection to balanced stochastic realizations.

UR - https://nsuworks.nova.edu/gscis_facarticles/421

U2 - 10.1109/9.24212

DO - 10.1109/9.24212

M3 - Article

SN - 0018-9286

VL - 34

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

ER -

A Note on a Cross Riccatian and Related Properties for Symmetric Stochastic Realizations

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