Detail publikace

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

Originální název

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

Anglický název

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

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

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"
}