A question about Algebraic Riccatti Equations

Hi, guys:

I wonder if Matlab is able to find all the solutions for the algebraic Riccatti equation appearing in Kalman Filter. The equation (system) is given by:

X=A*X*A'+B*B'-(A*X*C'+B*D')*(C*X*C'+D*D')^(-1)*(A*X*C'+B*D')'
Omega0=C*X*C'+D*D'
Omega1=A*X*C'+B*D'

In the above system, all variables are matrices. A,C, Omega0 and Omega1 are known, but X, B, and D are unknowns. We can substitute B and D to write the above system as a single equation on X. X corresponds to the (large-sample) forecast error variance matrix in the Kalman filter context.

X=0 is A solution to this system, and it is the idea behind Kalman filter that the forecast error matrix converges to zero when we have more observations. However, X=0 is not the unique solution and I want to find all the other solutions.

If you know some references about this issue, I really appreciate them.

Best,

Jing