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

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2 Author(s)
Ramos, J.A. ; United Technol. Opt. Syst. Inc., W. Palm Beach, FL, USA ; Verriest, E.I.

Recent results concerning cross Grammians for both SISO (single-input, single-output) and symmetric MIMO (multi-input, multioutput) 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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Automatic Control, IEEE Transactions on  (Volume:34 ,  Issue: 5 )