Geodesic
Higher-Order Derivatives of Lyapunov Functions and Partial Boundedness of Solutions with Partially Controllable Initial Conditions
Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 883-893.

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

Certain sufficient criteria for the types of partial boundedness of solutions with partially controllable initial conditions are obtained in terms of higher-order derivatives of the Lyapunov functions.
Keywords: Lyapunov function, Lyapunov vector function, higher-order derivatives, boundedness of solutions with respect to part of the variables, partially controllable initial conditions. 
@article{MZM_2017_101_6_a8,
     author = {K. S. Lapin},
     title = {Higher-Order {Derivatives} of {Lyapunov} {Functions} and {Partial} {Boundedness} of {Solutions} with {Partially} {Controllable} {Initial} {Conditions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {883--893},
     publisher = {mathdoc},
     volume = {101},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a8/}
}
TY  - JOUR
AU  - K. S. Lapin
TI  - Higher-Order Derivatives of Lyapunov Functions and Partial Boundedness of Solutions with Partially Controllable Initial Conditions
JO  - Matematičeskie zametki
PY  - 2017
SP  - 883
EP  - 893
VL  - 101
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a8/
LA  - ru
ID  - MZM_2017_101_6_a8
ER  - 
%0 Journal Article
%A K. S. Lapin
%T Higher-Order Derivatives of Lyapunov Functions and Partial Boundedness of Solutions with Partially Controllable Initial Conditions
%J Matematičeskie zametki
%D 2017
%P 883-893
%V 101
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a8/
%G ru
%F MZM_2017_101_6_a8
K. S. Lapin. Higher-Order Derivatives of Lyapunov Functions and Partial Boundedness of Solutions with Partially Controllable Initial Conditions. Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 883-893. http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a8/

[1] T. Yoshizawa, “Liapunov's function and boundedness of solutions”, Funkcial. Ekvac., 2 (1959), 95–142 | MR | Zbl

[2] V. V. Rumyantsev, A. S. Oziraner, Ustoichivost i stabilizatsiya dvizheniya otnositelno chasti peremennykh, Nauka, M., 1987 | MR | Zbl

[3] V. I. Vorotnikov, “Ob ustoichivosti i ustoichivosti po chasti peremennykh chastichnykh polozhenii ravnovesiya nelineinykh dinamicheskikh sistem”, Dokl. AN, 389:3 (2003), 332–337 | MR

[4] V. I. Vorotnikov, Yu. G. Martyshenko, “K zadache chastichnoi detektiruemosti nelineinykh dinamicheskikh sistem”, Avtomat. i telemekh., 2009, no. 1, 25–38 | MR | Zbl

[5] V. I. Vorotnikov, Yu. G. Martyshenko, “K teorii chastichnoi ustoichivosti nelineinykh dinamicheskikh sistem”, Izv. RAN. Teor. sist. upravl., 2010, no. 5, 23–31 | MR | Zbl

[6] V. I. Vorotnikov, Yu. G. Martyshenko, “K zadacham chastichnoi ustoichivosti dlya sistem s posledeistviem”, Tr. IMM UrO RAN, 19, no. 1, 2013, 49–58 | MR

[7] V. I. Vorotnikov, Yu. G. Martyshenko, “Ob ustoichivosti po chasti peremennykh “chastichnykh” polozhenii ravnovesiya sistem s posledeistviem”, Matem. zametki, 96:4 (2014), 496–503 | DOI | MR | Zbl

[8] E. V. Schennikova, “Ustoichivopodobnye svoistva reshenii odnoi mnogosvyaznoi sistemy differentsialnykh uravnenii”, Matem. zametki, 91:1 (2012), 136–142 | DOI

[9] A. V. Schennikov, “Printsip vklyucheniya i ustoichivopodobnye svoistva “chastichnogo” polozheniya ravnovesiya dinamicheskikh sistem”, Vestn. SPbGU. Ser. 10. Prikl. matem. Inform. Prots. upravl., 2011, no. 4, 119–132

[10] K. S. Lapin, “Chastichnaya ravnomernaya ogranichennost reshenii sistem differentsialnykh uravnenii s chastichno kontroliruemymi nachalnymi usloviyami”, Differents. uravneniya, 50:3 (2014), 309–316 | DOI | MR | Zbl

[11] K. S. Lapin, “Ogranichennost v predele reshenii sistem differentsialnykh uravnenii po chasti peremennykh s chastichno kontroliruemymi nachalnymi usloviyami”, Differents. uravneniya, 49:10 (2013), 1281–1286 | MR | Zbl

[12] E. V. Schennikova, “Funktsii Lyapunova i ogranichennost v predele otnositelno chasti peremennykh”, Matem. modelirovanie, 9:10 (1997), 24

[13] K. S. Lapin, “Ravnomernaya ogranichennost reshenii sistem differentsialnykh uravnenii po chasti peremennykh s chastichno kontroliruemymi nachalnymi usloviyami”, Matem. zametki, 96:3 (2014), 393–404 | DOI | Zbl

[14] K. S. Lapin, “Chastichnaya totalnaya ogranichennost reshenii sistem differentsialnykh uravnenii s chastichno kontroliruemymi nachalnymi usloviyami”, Matem. zametki, 99:2 (2016), 239–247 | DOI | MR | Zbl

[15] R. Z. Abdullin, L. Yu. Anapolskii, A. A. Voronov, A. S. Zemlyakov, R. I. Kozlov, A. I. Malikov, V. M. Matrosov, Metod vektornykh funktsii Lyapunova v teorii ustoichivosti, Nauka, M., 1987 | MR | Zbl

[16] V. M. Matrosov, Metod vektornykh funktsii Lyapunova: analiz dinamicheskikh svoistv nelineinykh sistem, Fizmatlit, M., 2001 | Zbl