Deviation of a set of trajectories from the state of equilibrium

1Martynyuk, AA
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2017, 10:10-17
https://doi.org/10.15407/dopovidi2017.10.010
Section: Mathematics
Language: Russian
Abstract: 

Estimates of the deviation of a set of trajectories from an equilibrium state are obtained for a family of differential equations. These estimates can be applied to the study of the stability of motion like the case of systems of ordinary diffe rential equatians.

Keywords: deviation of trajectories, set of equations, state of equilibrium
References: 
  1. Babenko, E. A. & Martynyuk, A. A. (2016). On stabilization of motion of affine systems. Int. Appl. Mech., 52, No. 4, pp. 100—108. https://doi.org/10.1007/s10778-016-0766-2
  2. Bellman, R. (1953). Stability Theory of Differential Equations. New York: McGraw-Hill Book Company.
  3. Lovartassi, Y., El Mazoudi, El. H. & Elalami, N. (2012). A new generalization of lemma Gronwall–Bellman. Appl. Math. Sci. 6, No. 13, pp. 621—628.
  4. Lakshmikantham, V., Leela, S. & Devi, V. (2005). Theory of Set Differential Equations in Metric Space. Cambridge: Cambridge Scientific Publishers.
  5. Martynyuk, A. A. (2015). Novel bounds for solutions of nonlinear differential equations. Applied Math., 6, pp. 182—194. https://doi.org/10.4236/am.2015.61018
  6. Martynyuk, A. A., Babenko, E. A. (2016). Finite time stability of uncertain affine systems. Math. Eng. Sci. Aerospace, 7, No. 1, pp. 179—196.
  7. Martynyuk, A. A. & Martynyuk-Chernienko, Yu. A. (2012). Uncertain Dynamical Systems: Stability and Motion Control. Boca Raton: CRC Press, Taylor and Francis Group.
  8. N'Doye, I. (2011). Generalisation du lemme de Gronwall-Bellman pour la stabilisation des systemes fractionnaires. (PhD These). Nancy-Universite.