  Recently, a max-plus dual space fundamental solution semigroup for a class of
difference Riccati equation (DRE) has been developed. This fundamental solution
semigroup is represented in terms of the kernel of a specific max-plus linear
operator that plays the role of the dynamic programming evolution operator in a
max-plus dual space. In order to fully understand connections between this dual
space fundamental solution semigroup and evolution of the value function of the
underlying optimal control problem, a new max-plus primal space fundamental
solution semigroup for the same class of difference Riccati equations is
presented. Connections and commutation results between this new primal space
fundamental solution semigroup and the recently developed dual space
fundamental solution semigroup are established.
