  We aim at providing a characterization of the ability to maintain a
stochastic coupled system with porous media components in a prescribed set of
constraints by using internal controls. This property is proven via a
quasi-tangency local-in-time condition in the spirit of Euler approximation
schemes. In particular, by employing one of the components of the system as
asymptotic supervisor, we give conditions guaranteeing the exponential
asymptotic stabilizability of controlled porous media equations.
