Superposition laws for solutions of differential matrix Riccati equations arising in control theory

Representation formulas are given for the general solution of the
N \times N
matrix Riccati equation
\dot{W} = A + WB + CW + WDW
using
n
known solutions, with
n = 1, ..., 5
(
n
-representations). The 5- representation is a superposition formula, in that it expresses the general solution explicitly as a function of five particular solutions and N
²
arbitrary constants (
N \geq 2
), using no further information. The representation formulas can be used in numerical calculations. The 4- and 5- representations are specially useful when a solution
W(t)
has a singularity for some finite
t = t_{0}
. They also clarify the properties of the solution space: the matrix elements of
W(t)
are meromorphic functions of
t
having simple poles as the only possible singularities. The relation between the representation formulas and previously known results is discussed.