Geodesic
Lyapunov --- Krasovskii functionals for homogeneous systems with multiple delays
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 2, pp. 183-195

Voir la notice de l'article provenant de la source Math-Net.Ru

In this article, explicit constructions of Lyapunov — Krasovskii functionals are proposed for homogeneous systems with multiple constant delays and homogeneity degree of the right-hand sides strictly greater than one. The constructions are based on the Lyapunov functions suitable for the analysis of corresponding systems with all delays equal to zero. The letter systems are assumed to be asymptotically stable. It is proved that the proposed functionals satisfy the conditions of the Krasovskii theorem, and hence it allows us to establish the asymptotic stability of the trivial solution for arbitrary values of delays. The functionals are applied to the estimation of the attraction region of the trivial solution.
Keywords: time delay systems, homogeneous systems, asymptotic stability, Lyapunov — Krasovskii functionals, attraction region. 
@article{VSPUI_2021_17_2_a7,
     author = {I. V. Alexandrova and A. P. Zhabko},
     title = {Lyapunov --- {Krasovskii} functionals for homogeneous systems with multiple delays},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {183--195},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2021_17_2_a7/}
}
TY  - JOUR
AU  - I. V. Alexandrova
AU  - A. P. Zhabko
TI  - Lyapunov --- Krasovskii functionals for homogeneous systems with multiple delays
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2021
SP  - 183
EP  - 195
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2021_17_2_a7/
LA  - ru
ID  - VSPUI_2021_17_2_a7
ER  - 
%0 Journal Article
%A I. V. Alexandrova
%A A. P. Zhabko
%T Lyapunov --- Krasovskii functionals for homogeneous systems with multiple delays
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2021
%P 183-195
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSPUI_2021_17_2_a7/
%G ru
%F VSPUI_2021_17_2_a7
I. V. Alexandrova; A. P. Zhabko. Lyapunov --- Krasovskii functionals for homogeneous systems with multiple delays. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 2, pp. 183-195. http://geodesic.mathdoc.fr/item/VSPUI_2021_17_2_a7/