Flatness and Submersivity of Discrete-Time Dynamical Systems

This letter addresses flatness of discrete-time systems called difference flatness. A definition of flatness, that encompasses the standard ones, in particular backward and forward difference flatness, is introduced. It also allows to cope with systems which are not necessarily controllable or submersive. Besides, it considers nonlinear dynamical systems defined on general sets (without necessary special structures) which can be either continuous or discrete. Based on this definition, a result is established and stipulates that a flat and submersive nonlinear system is fully reachable (which is equivalent to fully controllable). Next, the special case of linear systems is considered leading to a necessary and sufficient condition.