Keywords: mechanical systems, dynamical systems, motion stability, Lyapunov functions, iteration method, differential inequalities sequence, transient process functional estimates
Acknowledgements. This work was supported by the RFBR Grants 16-08-00997, 17-01-00672.
References
1. Melnikov G.I. Some problems of the direct Lyapunov method. Doklady Akademii Nauk, 1956, vol. 110, pp. 326–329. (In Russian)
2. Matrosov V.M., Anapol'skii L.Yu., Vassilyev S.N. Method of Comparison in the Mathematical Theory of Systems. Novosibirsk, Nauka Publ., 1980, 480 p. (In Russian)
3. Vassilyev S.N. To the 80th anniversary of the birth of Academician V.M. Matrosov. Avtomatika i Telemekhanika, 2013, no. 2, pp. 139–151. (In Russian)
4. Vassilyev S.N., Kosov A.A. Common and multiple Lyapunov functions in stability analysis of nonlinear switched systems. AIP Conference Proc., 2012, vol. 1493, pp. 1066–1073. doi: 10.1063/1.4765620
5. Vassilyev S.N. The reduction method, I. Nonlinear Analysis, Theory, Methods and Applications, 2006, vol. 64, no. 2, pp. 242–253. doi: 10.1016/j.na.2005.06.047
6. Martynyuk A.A., Martynyuk-Chernienko Y.A. Analysis of the set of trajectories of nonlinear dynamics: stability and boundedness of motions. Differential Equations, 2013, vol. 49, no. 1, pp. 20–31. doi: 10.1134/s0012266113010035
7. Martynyuk A.A. On the theory of Lyapunov's direct method. Doklady Mathematics, 2006, vol. 73, no. 3, pp. 376–379. doi: 10.1134/s1064562406030161
8. Melnikov G.I., Ivanov S.E., Melnikov V.G., Malykh K.S. Application of modified conversion method to a nonlinear dynamical system. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2015, vol. 15, no. 1, pp. 149–154. doi: 10.17586/2226-1494-2015-15-1-149-154 (In Russian)
9. Ivanov S.E., Melnikov G.I. Off-line interaction of the nonlinear dynamic systems. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2014,
no. 1, pp. 151–156.
10. Ivanov S.E. Algorithmic realization for research method of the nonlinear dynamic systems Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2012, no. 4, pp. 90–92. (In Russian)
11. Melnikov V.G. Transformation of dynamic polynomial systems by Chebyshev approximation. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2012, no. 4, pp. 85–90. (In Russian)
12. Melnikov G.I. Dinamika Nelineinykh Mekhanicheskikh i Elektromekhanicheskikh Sistem [Nonlinear Dynamics of Mechanical and Electromechanical Systems]. Leningrad, Mashinostroenie Publ., 1975, 198 p. (In Russian)
13. Lakshmikantham V., Matrosov V.M., Sivasundaram S. Vector Lyapunov Functions Method in Stability Theory. Amsterdam, Kluwer Academic Publishers, 1991, 172 p. doi: 10.1007/978-94-015-7939-1
14. Aleksandrov A.Yu., Tikhonov A.A. Electrodynamic stabilization of earth-orbiting satellites in equatorial orbits. Cosmic Research, 2012, vol. 50, no. 4, pp. 313–318. doi: 10.1134/s001095251203001x
15. Kovalev A.M., Martynyuk A.A., Boichuk O.A., Mazko A.G., Petryshyn R.I., Slyusarchuk V.Y., Zuyev A.L., Slyn'ko V.I. Novel qualitative methods of nonlinear mechanics and their application to the analysis of multifrequency oscillations, stability, and control problems. Nonlinear Dynamics and Systems Theory, 2009, vol. 9, no. 2, pp. 117–145.
16. Sugie J., Hata S. Global asymptotic stability for half-linear differential systems with generalized almost periodic coefficients. Monatshefte fur Mathematik, 2012, vol. 166, no. 2, pp. 255–280. doi: 10.1007/s00605-011-0297-1