On the Local Cone Ẋ(x) of realizable state-velocities ẋ for controlled dynamical systems

The concept of the “cone Ẋ(x) of all realizable state-velocity values” ẋ at each x in state-space, is used to characterize important geometric properties of state-trajectories x(t) for controlled dynamical systems. The results are useful in discovering invisible “barriers” in state-space across which controlled state-trajectories cannot pass. The new concept of hyper-controllability is introduced and its usefulness is explored for the case of time-invariant, linear dynamical systems.