  A class of differential Riccati equations (DREs) is considered whereby the
evolution of any solution can be identified with the propagation of a value
function of a corresponding optimal control problem arising in L2-gain
analysis. By exploiting the semigroup properties inherited from the attendant
dynamic programming principle, a max-plus primal space fundamental solution
semigroup of max-plus linear max-plus integral operators is developed that
encapsulates all such value function propagations. Using this semigroup, a new
one-parameter fundamental solution semigroup of matrices is developed for the
aforementioned class of DREs. It is demonstrated that this new semigroup can be
used to compute particular solutions of these DREs, and to characterize finite
escape times (should they exist) in a relatively simple way compared with that
provided by the standard symplectic fundamental solution semigroup.
