Publication result detail

Optimal stabilization for differential systems with delays - Malkin’s approach

DEMCHENKO, H.; DIBLÍK, J.; KHUSAINOV, D.

Original Title

Optimal stabilization for differential systems with delays - Malkin’s approach

English Title

Optimal stabilization for differential systems with delays - Malkin’s approach

Type

WoS Article

Original Abstract

The paper considers a process controlled by a system of delayed differential equations. Under certain assumptions, a control function is determined such that the zero solution of the system is asymptotically stable and, for an arbitrary solution, the integral quality criterion with infinite upper limit exists and attains its minimum value in a given sense. To solve this problem, Malkin’s approach to ordinary differential systems is extended to delayed functional differential equations, and Lyapunov’s second method is applied. The results are illustrated by examples, and applied to some classes of delayed linear differential equations.

English abstract

The paper considers a process controlled by a system of delayed differential equations. Under certain assumptions, a control function is determined such that the zero solution of the system is asymptotically stable and, for an arbitrary solution, the integral quality criterion with infinite upper limit exists and attains its minimum value in a given sense. To solve this problem, Malkin’s approach to ordinary differential systems is extended to delayed functional differential equations, and Lyapunov’s second method is applied. The results are illustrated by examples, and applied to some classes of delayed linear differential equations.

Keywords

Differential equation; delay; control; quality criterion; asymptotic stability

Key words in English

Differential equation; delay; control; quality criterion; asymptotic stability

Authors

DEMCHENKO, H.; DIBLÍK, J.; KHUSAINOV, D.

RIV year

2020

Released

19.04.2019

Publisher

Elsevier

Location

PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND

ISBN

0016-0032

Periodical

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS

Volume

356

Number

8

State

United States of America

Pages from

4811

Pages to

4841

Pages count

31

URL

https://www.sciencedirect.com/science/article/abs/pii/S0016003219302698?via%3Dihub

BibTex

@article{BUT160033,
  author="Hanna {Demchenko} and Josef {Diblík} and Denys {Khusainov}",
  title="Optimal stabilization for differential systems with delays - Malkin’s approach",
  journal="JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS",
  year="2019",
  volume="356",
  number="8",
  pages="4811--4841",
  doi="10.1016/j.jfranklin.2019.04.021",
  issn="0016-0032",
  url="https://www.sciencedirect.com/science/article/abs/pii/S0016003219302698?via%3Dihub"
}