For the bilinear control system of the form , with essentially nonnegative and constant diagonal matrices, the following global controllability question is studied: when can any two points in with positive coordinates be connected by a trajectory of this system? The answers for and for any are given; some necessary conditions for other cases are proven.
Title: On Positive Orthant Controllability of Bilinear Systems in Small Codimensions
Authors: Yu. L. Sachkov
Journal title: SIAM Journ. Control and Optimization