Geodesic
Positive orthant scalar controllability of bilinear systems
Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 419-424.

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For the bilinear control system $\dot x=(A+uB)x$, $x\in\mathbb R^n$, $u\in\mathbb R$ 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 $\mathbb R^n$ are constructed that are intersected by all the trajectories of the system in one direction. 
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     author = {Yu. L. Sachkov},
     title = {Positive orthant scalar controllability of bilinear systems},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a9/}
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Yu. L. Sachkov. Positive orthant scalar controllability of bilinear systems. Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 419-424. http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a9/

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