# Yu. L. Sachkov, On Positive Orthant Controllability of Bilinear Systems in Small Codimensions

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.