# Yu. L. Sachkov, Positive Orthant Controllability of Single-input Bilinear Systems

Title: Positive orthant scalar controllability of bilinear systems
Authors: Yu. L. Sachkov
Journal title: Mathematical Notes
Year: 1995
Issue: 3
Volume: 58
Pages: 966–969
Citation:

Yu. L. Sachkov, Positive orthant scalar controllability of bilinear systems, Mathematical Notes, 1995, 58:3, 966–969.

Abstract:

For the bilinear control system $\dot{x}=(A+u\ B )x, x \in R^n, u \in R,\$ where $A\$ is an $\ n \times n$ essentially nonnegative matrix, and $B$ is a diagonal matrix, the following controllability problem is investigated: can any two points with positive coordinates be joined by a trajectory of the system? For $n>2 \$, the answer is negative in the generic case: hypersurfaces in $R^n$ are constructed that are intersected by all the trajectories of the system in one direction.