Geodesic
On the construction of Lyapunov's function
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1987), pp. 39-45.

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The problem of stability of the system of non-linear stationary differential equations is considered when perturbating forces of small integral act on the system during finite time interval. By means of Lyapunov’s functions necessary and sufficient conditions have been obtained for linear stationary systems in case of which the system is stable for any acting forces [1]. The sufficient conditions in case of which the non-linear system is stable for any acting forces have been defined. A concrete example has been constructed where the system becomes instable when the mentioned conditions are not kept. 
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M. S. Gabrielyan; S. G. Shahinyan. On the construction of Lyapunov's function. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (1987), pp. 39-45. http://geodesic.mathdoc.fr/item/UZERU_1987_1_a6/

[1] S. G. Shaginyan, “Ob odnoi zadache teorii ustoichivosti”, Uchenye zapiski EGU, 1986, no. 2 | MR | Zbl

[2] F. R. Gantmakher, Teoriya matrits, Nauka, Moskva, 1967

[3] A. M. Lyapunov, Obschaya zadacha ob ustoichivosti dvizheniya, Moskva, Gostekhizdat, 1950, 472 pp. | MR

[4] E. A. Barbashin, N. N. Krasovskii, “O suschestvovanii funktsii Lyapunova v sluchae asimptoticheskoi ustoichivosti v tselom”, Prikl. mat. i mekhanika, 18:3 (1954), 345–350 | Zbl