Yurchenko I.V., Yasynskyy V.K.
The existence of Lyapunov–Krasovskii functionals for stochastic differential-functional Ito–Skorokhod equations under the condition of the solutions stability on probability with finite aftereffect

In the paper, it is established that Lyapunov–Krasovskii functionals with definite properties exist for dynamic systems of random structure with finite prehistory and with the property of one or another probability stability. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: aftereffect, Lyapunov–Krasovskii functionals, stability, systems of random structure, Convergence of numerical methods, Stochastic systems, aftereffect, Finite aftereffect, Functionals, Random structures, System stability

Cite:
Yurchenko I.V., Yasynskyy V.K. (2018). The existence of Lyapunov–Krasovskii functionals for stochastic differential-functional Ito–Skorokhod equations under the condition of the solutions stability on probability with finite aftereffect. Cybernetics and Systems Analysis, 54 (6), 119-133. doi: https://doi.org/10.1007/s10559-018-0099-8 http://jnas.nbuv.gov.ua/article/UJRN-0000926959 [In Russian].