A necessary controllability condition for discrete-time systems

Proposes a geometric approach for analyzing discrete-time nonlinear system controllability. The main idea takes issue from a minimum principle application developed for the determination of the controllable set boundary for continuous time system. The purpose here is different and consists of exhibiting a condition for the non-existence of a boundary control set, giving by this way a necessary condition for the complete controllability of the system under investigation. This condition is shown to be equivalent to the necessary and sufficient condition given by the application of Kalman controllability criteria for linear systems. This approach is finally used to check controllability for a discrete-time nonlinear model of an electrically stimulated muscle.