Research of the asymptotic equilibrium of time-delay systems by junction of Lyapunov --- Krasovskii and Razumikhin approaches
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 2, pp. 198-208
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The nonlinear time-delay systems are considered and the limiting behavior of their solutions is investigated. The case in which the solutions have a trivial equilibrium that may not be an invariant set of the system is studied. The junction of Lyapunov — Krasovskii and Razumikhin approaches is applied to obtain sufficient conditions for the existence of an asymptotic quiescent position in the large. In the case when a general system has a trivial solution, new sufficient conditions for its asymptotic stability are obtained. Examples, that illustrate the application of the obtained results, are given.
Keywords:
time-delay systems, asymptotic stability, asymptotic quiescent position, Lyapunov — Krasovskii functionals.
@article{VSPUI_2022_18_2_a0,
author = {S. E. Kuptsova and S. Yu. Kuptsov},
title = {Research of the asymptotic equilibrium of time-delay systems by junction of {Lyapunov} --- {Krasovskii} and {Razumikhin} approaches},
journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
pages = {198--208},
publisher = {mathdoc},
volume = {18},
number = {2},
year = {2022},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VSPUI_2022_18_2_a0/}
}
TY - JOUR AU - S. E. Kuptsova AU - S. Yu. Kuptsov TI - Research of the asymptotic equilibrium of time-delay systems by junction of Lyapunov --- Krasovskii and Razumikhin approaches JO - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ PY - 2022 SP - 198 EP - 208 VL - 18 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VSPUI_2022_18_2_a0/ LA - en ID - VSPUI_2022_18_2_a0 ER -
%0 Journal Article %A S. E. Kuptsova %A S. Yu. Kuptsov %T Research of the asymptotic equilibrium of time-delay systems by junction of Lyapunov --- Krasovskii and Razumikhin approaches %J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ %D 2022 %P 198-208 %V 18 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/VSPUI_2022_18_2_a0/ %G en %F VSPUI_2022_18_2_a0
S. E. Kuptsova; S. Yu. Kuptsov. Research of the asymptotic equilibrium of time-delay systems by junction of Lyapunov --- Krasovskii and Razumikhin approaches. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 2, pp. 198-208. http://geodesic.mathdoc.fr/item/VSPUI_2022_18_2_a0/