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

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


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.