On the small-time controllability of discontinuous piece-wise linear systems

This note presents a necessary and sufficient condition for small time controllability of a specific class of piece-wise linear systems. These systems are linear in four areas determined in the state space by two hyperplanes with a nonempty intersection. On the hyperplanes the systems appear to be discontinuous. Our main result extends the classical Kalman criterion for controllability to the case of piece-wise linear control systems with controls taking values in closed convex cones.