Geodesic
On global Lyapunov reducibility of two-dimensional linear time-invariant control systems
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 25 (2002) no. 2, pp. 47-50.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let the stationary system $\dot x=Ax+Bu, x\in\mathbb{R}^2, u\in\mathbb{R}^m$ is totally controllable. Then it possesses the property of global Lyapunov reducibility in class of stationary controls $u=Ux$, that is for any fixed stationary system $\dot y=Cy$ there exists the time-independent matrix $U$, such that the system $\dot x=(A+BU)x$ with this matrix is asymptotically equivalent (kinematically similar) to the above fixed system. 
@article{IIMI_2002_25_2_a11,
     author = {V. A. Zaitsev},
     title = {On global {Lyapunov} reducibility of two-dimensional linear time-invariant control systems},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {47--50},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2002_25_2_a11/}
}
TY  - JOUR
AU  - V. A. Zaitsev
TI  - On global Lyapunov reducibility of two-dimensional linear time-invariant control systems
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2002
SP  - 47
EP  - 50
VL  - 25
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2002_25_2_a11/
LA  - ru
ID  - IIMI_2002_25_2_a11
ER  - 
%0 Journal Article
%A V. A. Zaitsev
%T On global Lyapunov reducibility of two-dimensional linear time-invariant control systems
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2002
%P 47-50
%V 25
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2002_25_2_a11/
%G ru
%F IIMI_2002_25_2_a11
V. A. Zaitsev. On global Lyapunov reducibility of two-dimensional linear time-invariant control systems. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 25 (2002) no. 2, pp. 47-50. http://geodesic.mathdoc.fr/item/IIMI_2002_25_2_a11/

[1] Makarov E. K., Popova S. N., “O globalnoi upravlyaemosti polnoi sovokupnosti lyapunovskikh invariantov dvumernykh lineinykh sistem”, Differents. uravneniya, 35:1 (1999), 97–106 | MR | Zbl

[2] Zaitsev V. A., “Globalnaya lyapunovskaya privodimost dvumernykh upravlyaemykh sistem s kusochno-postoyannymi koeffitsientami”, Vestn. Udm. un-ta, 2002, no. 1, 3–12 | Zbl

[3] Popov V. M., Giperustoichivost avtomaticheskikh sistem, Nauka, M., 1970, 456 pp. | MR