A note on the cross Riccatian and related properties for symmetric stochastic realizations

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IEEE Transactions on Automatic Control, ISSN: 0018-9286, Vol: 34, Issue: 5, Page: 548-551

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Ramos, Jose A.; Verriest, Erik I.
Institute of Electrical and Electronics Engineers (IEEE); NSUWorks
Computer Science; Engineering; Computer Sciences
article description
Recent results concerning cross Grammians for both SISO 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. © 1989 IEEE