Differential controllability and the solution of linear inequalities--Part I

Two characterizations of differentially controllable linear autonomous systems for which the origin is assumed to be a boundary point of the control restraint set are presented. These characterizations extend well-known results which contain the assumption that the origin is interior to the control restraint set. These characterizations are given in terms of the system matrix and the control restraint set. The first theorem applies to arbitrary restraint sets, while the second is restricted to polyhedral regions. The second characterization is the basis for a computational algorithm for the determination of differential controllability to be described in a future paper.