On the Local Cone ( ) Xxof Realizable State- Velocities for Controlled Dynamical Systems x

The concept of the "cone ( ) X x � of all realizable state-velocity values" at each x in state-space, is used to characterize important geometric properties of state- trajectories x� ( ) t x 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.