Publication result detail

Stability, unevenly with delay, one of weak linear system with an aftereffect.

BAŠTINEC, J.; DIBLÍK, J.; KHUSAINOV, D.; SIRENKO, A.

Original Title

Stability, unevenly with delay, one of weak linear system with an aftereffect.

English Title

Stability, unevenly with delay, one of weak linear system with an aftereffect.

Type

Peer-reviewed article not indexed in WoS or Scopus

Original Abstract

We consider system of differential equations with asymptotically stable diagonal part and the nonlinearity, representing the sum of non-linear functions one of the variable, which satisfying Lipschitz conditions. The system has a position of equilibrium in the first quadrant. Studying of the stability of the equilibrium position is conducted with using the method of Lyapunov functions. The Lyapunov function is building as sum of the squares of the phase variables. We get constructive conditions of stability. We considering systems with delay. We obtain sufficient conditions of stability, which depends on the magnitude of the delay.

English abstract

We consider system of differential equations with asymptotically stable diagonal part and the nonlinearity, representing the sum of non-linear functions one of the variable, which satisfying Lipschitz conditions. The system has a position of equilibrium in the first quadrant. Studying of the stability of the equilibrium position is conducted with using the method of Lyapunov functions. The Lyapunov function is building as sum of the squares of the phase variables. We get constructive conditions of stability. We considering systems with delay. We obtain sufficient conditions of stability, which depends on the magnitude of the delay.

Keywords

nonlinear systems, stability, the equilibrium position, the method of Lyapunov functions, system with delay, condition B. S. Razumikhin.

Key words in English

nonlinear systems, stability, the equilibrium position, the method of Lyapunov functions, system with delay, condition B. S. Razumikhin.

Authors

BAŠTINEC, J.; DIBLÍK, J.; KHUSAINOV, D.; SIRENKO, A.

RIV year

2017

Released

16.05.2016

Publisher

NAV Ukrajiny

Location

Kyjev, Ukrajina

ISBN

1683-4720

Periodical

Trudy NAN Ukrainy

Volume

29

Number

1

State

Ukraine

Pages from

129

Pages to

146

Pages count

18

BibTex

@article{BUT125132,
  author="Jaromír {Baštinec} and Josef {Diblík} and Denys {Khusainov} and Andrii {Sirenko}",
  title="Stability, unevenly with delay, one of weak linear system with an aftereffect.",
  journal="Trudy NAN Ukrainy",
  year="2016",
  volume="29",
  number="1",
  pages="129--146",
  issn="1683-4720"
}

Documents

125132