Geodesic
On global Lyapunov reducibility of two-dimensional linear time-invariant control systems
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 2 (2002), pp. 47-50 
V. A. Zaitsev. On global Lyapunov reducibility of two-dimensional linear time-invariant control systems. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, no. 2 (2002), pp. 47-50. http://geodesic.mathdoc.fr/item/IIMI_2002_2_a11/
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     title = {On global {Lyapunov} reducibility of two-dimensional linear time-invariant control systems},
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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.

[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