Immersion of nonlinear systems into higher order systems

Two nonlinear systems having the same number of inputs, but not the same number of state variables, are considered. The problem of the existence of two invertible state feedback laws and a surjective mapping from the higher dimensional state space of one system into the lower dimensional state space of the second system is stated, such that the rst system dynamics reduces exactly to the second system dynamics. This problem generalizes the linear feedback equivalence problem of two systems and is fully solved in the special case of feedback linearizable systems.