Publication 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

journal article in Web of Science

Language

en

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

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

Year of study

356

Number

8

State

US

Pages from

4811

Pages to

4841

Pages count

31

URL

Documents

BibTex


@article{BUT160033,
  author="Hanna {Demchenko} and Josef {Diblík} and Denys {Khusainov}",
  title="Optimal stabilization for differential systems with delays - Malkin’s approach",
  annote="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.",
  address="Elsevier",
  chapter="160033",
  doi="10.1016/j.jfranklin.2019.04.021",
  howpublished="print",
  institution="Elsevier",
  number="8",
  volume="356",
  year="2019",
  month="april",
  pages="4811--4841",
  publisher="Elsevier",
  type="journal article in Web of Science"
}