Title: On Positive Orthant Controllability of Bilinear Systems in Small Codimensions

Authors: Yu. L. Sachkov

Journal title: SIAM Journ. Control and Optimization

Year: 1997

Volume: 35

Pages: 29—35

Abstract:

For the bilinear control system of the form $$\dot{x} = (A + \sum_{i=1}^m u_i B_i) x, \ x \in R^n, \ u_i \in R$$, with $$A$$ essentially nonnegative and $$B_i$$ constant diagonal matrices, the following global controllability question is studied: when can any two points in $$R^n$$ with positive coordinates be connected by a trajectory of this system? The answers for $$\ m = n-1\ $$ and $$\ m=n-2\ $$ for any $$\ n > 2\ $$ are given; some necessary conditions for other cases are proven.