A note on a cross Riccatian and related properties for symmetric stochastic realizations
José A. Ramos, Erik I. Verriest · 1987
Recent results concerning cross Grammians for both SISO and symmetric MIMO systems are extended for 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 symmtry properties similar to those for the cross Grammian are introduced, along with connections to balanced stochastic realizations.