Deviation of a set of trajectories from the state of equilibrium

Authors

  • A.A. Martynyuk S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kiev

DOI:

https://doi.org/10.15407/dopovidi2017.10.010

Keywords:

deviation of trajectories, set of equations, state of equilibrium

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.

Downloads

References

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

Bellman, R. (1953). Stability Theory of Differential Equations. New York: McGraw-Hill Book Company.

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.

Lakshmikantham, V., Leela, S. & Devi, V. (2005). Theory of Set Differential Equations in Metric Space. Cambridge: Cambridge Scientific Publishers.

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

Martynyuk, A. A., Babenko, E. A. (2016). Finite time stability of uncertain affine systems. Math. Eng. Sci. Aerospace, 7, No. 1, pp. 179—196.

Martynyuk, A. A. & Martynyuk-Chernienko, Yu. A. (2012). Uncertain Dynamical Systems: Stability and Motion Control. Boca Raton: CRC Press, Taylor and Francis Group.

N'Doye, I. (2011). Generalisation du lemme de Gronwall-Bellman pour la stabilisation des systemes fractionnaires. (PhD These). Nancy-Universite.

Published

21.09.2024

How to Cite

Martynyuk, A. (2024). Deviation of a set of trajectories from the state of equilibrium . Reports of the National Academy of Sciences of Ukraine, (10), 10–17. https://doi.org/10.15407/dopovidi2017.10.010

Most read articles by the same author(s)

1 2 > >>