In-block controllability of affine systems on polytopes

The paper introduces the study of in-block controllability (IBC) of affine systems on polytopes. In particular, we study whether all the states in the interior of a given polytope are mutually accessible through its interior by applying uniformly bounded control inputs. We first provide easily checkable necessary conditions for IBC. Then, for an important class of polytopes, simplicial polytopes, we show that these conditions are also sufficient. Several illustrative examples are also given to clarify the main results.