Geodesic
Positive orthant scalar controllability of bilinear systems
Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 419-424 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{MZM_1995_58_3_a9,
     author = {Yu. L. Sachkov},
     title = {Positive orthant scalar controllability of bilinear systems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {419--424},
     year = {1995},
     volume = {58},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a9/}
}
TY  - JOUR
AU  - Yu. L. Sachkov
TI  - Positive orthant scalar controllability of bilinear systems
JO  - Matematičeskie zametki
PY  - 1995
SP  - 419
EP  - 424
VL  - 58
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a9/
LA  - ru
ID  - MZM_1995_58_3_a9
ER  - 
%0 Journal Article
%A Yu. L. Sachkov
%T Positive orthant scalar controllability of bilinear systems
%J Matematičeskie zametki
%D 1995
%P 419-424
%V 58
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a9/
%G ru
%F MZM_1995_58_3_a9
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/

[1] Boothby W. M., “Some comments on positive orthant controllability of bilinear systems”, SIAM J. Control Optim., 20:5 (1982), 634–644 | DOI | MR | Zbl

[2] Sachkov Yu. L., “Upravlyaemost dvumernykh i trekhmernykh bilineinykh sistem v polozhitelnom ortante”, Differents. uravneniya, 29 (1993), 361–363 | MR | Zbl

[3] Bacciotti A., “On the positive orthant controllability of two-dimensional bilinear systems”, Systems and Control Lett., 3 (1983), 53–55 | DOI | MR | Zbl