Publication 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

journal article - other

Language

en

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.

Released

16.05.2016

Publisher

NAV Ukrajiny

Location

Kyjev, Ukrajina

ISBN

1683-4720

Periodical

Trudy NAN Ukrainy

Year of study

29

Number

1

State

UA

Pages from

129

Pages to

146

Pages count

18

Documents

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.",
  annote="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.",
  address="NAV Ukrajiny",
  chapter="125132",
  howpublished="print",
  institution="NAV Ukrajiny",
  number="1",
  volume="29",
  year="2016",
  month="may",
  pages="129--146",
  publisher="NAV Ukrajiny",
  type="journal article - other"
}