On solutions of the Riccati equation in optimization problems

The difference
D
between two solutions
S
and
M
of the matrix Riccati equation.
-\dot{M} = MA + A'M + MBM + C
is given by
D = RQ^{-1}R'
, where
-\dot{R} = (A+SB)R
and
-\dot{Q}= RBR'
. These relations can be used to evaluate
M(t)
for
t < T
arising in optimization problems in which
M(T)
does not exist. The relations can also be used to compare the solution of the Riccati equation with its asymptotic solution.