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.