Poisson reduction via feedback invariant distributions

The reduction of Poisson structures on the state space of controlled Hamiltonian system is studied. The existence of completely integrable feedback-invariant distributions gives rise to a collection of reduced Poisson structures on the quotient by maximal integrable submanifolds. In special cases we can define a Poisson subsystem, which is feedback invariant. The result is an initial step towards the development of a normal form for controlled Hamiltonian system based on the information contained of the accessibility algebra.