A Note on a Cross Riccatian and Related Properties for Symmetric Stochastic Realizations
IEEE Transactions on Automatic Control
ISSN or ISBN
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.
Ramos, Jose A. and Verriest, Erik I., "A Note on a Cross Riccatian and Related Properties for Symmetric Stochastic Realizations" (1989). CEC Faculty Articles. 421.