Geodesic
The stabilization of program motions of firm body on a~moving platform
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 4, pp. 44-52.

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We consider firmbody with fixed point on amoving platform.We solve the problem of construction asimptotically stability programm motion. The programm motion can be any function. Control is received in the form the analytical solution. We solve the problem of stabilization by the direct Lyapunov's method and the method of limiting functions and systems. In this case we can use the Lyapunovs functions having constant signs derivatives. 
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S. P. Bezglasnyi; O. A. Mysina. The stabilization of program motions of firm body on a~moving platform. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 4, pp. 44-52. http://geodesic.mathdoc.fr/item/ISU_2008_8_4_a6/

[1] Afanasev V. N., Kolmanovskii V. B., Nosov V. R., Matematicheskaya teoriya konstruirovaniya sistem upravleniya, Vyssh. shk., M., 1989, 447 pp. | MR | Zbl

[2] Galiullin A. S., Mukhametzyanov I. A., Mukharlyamov R. G., Furasov V. D., Postroenie sistem programmnogo dvizheniya, Nauka, M., 1971, 352 pp. | MR | Zbl

[3] Zubov V. I., Problema ustoichivosti protsessov upravleniya, Sudostroenie, L., 1980, 375 pp. | MR | Zbl

[4] Rush N., Abets R., Lalua M., Pryamoi metod Lyapunova v teorii ustoichivosti, Mir, M., 1980, 301 pp. | MR

[5] Artstein Z., “Topological dynamics of an ordinary equations”, J. Differ. Equat., 23 (1977), 216–223 | DOI | MR | Zbl

[6] Andreev A. S., “Ob asimptoticheskoi ustoichivosti i neustoichivosti nulevogo resheniya neavtonomnoi sistemy”, PMM, 48:2 (1984), 225–232 | MR

[7] Smirnov E. Ya., Pavlikov I. Yu., Scherbakov P. P., Yurkov A. V., Upravlenie dvizheniem mekhanicheskikh sistem, Izd-vo LGU, L., 1985, 347 pp.

[8] Bezglasnyi S. P., “The stabilization of program motions of controlled nonlinear mechanical systems”, Korean J. Comput. and Appl. Math., 14:1–2 (2004), 251–266 | DOI | MR