  The article presents a rather surprising Floquet-type representation of
time-varying transition matrices associated with a class of nonlinear matrix
differential Riccati equations. The main difference with conventional Floquet
theory comes from the fact that the underlying flow of the solution matrix is
aperiodic. The monodromy matrix associated with this Floquet representation
coincides with the exponential (fundamental) matrix associated with the
stabilizing fixed point of the Riccati equation. The second part of this
article is dedicated to the application of this representation to the stability
of matrix differential Riccati equations. We provide refined global and local
contraction inequalities for the Riccati exponential semigroup that depend
linearly on the spectral norm of the initial condition. These refinements
improve upon existing results and are a direct consequence of the Floquet-type
representation, yielding what seems to be the first results of this type for
this class of models.
