Publication result detail

Exponential stability of linear discrete systems with multiple delays by degenerated Lyapunov-Krasovskii functionals

DIBLÍK, J.

Original Title

Exponential stability of linear discrete systems with multiple delays by degenerated Lyapunov-Krasovskii functionals

English Title

Exponential stability of linear discrete systems with multiple delays by degenerated Lyapunov-Krasovskii functionals

Type

WoS Article

Original Abstract

The problem of exponential stability of delayed discrete systems with multiple delays s n-ary sumation x(n + 1) = (I + A)x(n) + i=1 Bix(n - i), n = 0, 1, .. . is studied, where x = (x1 x2 ... xm)T is an unknown vector, m and s are fixed positive integers, A, Bi are square constant matrices and I is a unit matrix. A new degenerated Lyapunov-Krasovskii functional is used to derive sufficient conditions for exponential stability and to derive an exponential estimate of the norm of solutions. Though often used in the study of stability, the assumption that the spectral radius of the matrix of linear terms is less than 1 is not applied here. The criterion derived is illustrated by an example and compared with previously known results.

English abstract

The problem of exponential stability of delayed discrete systems with multiple delays s n-ary sumation x(n + 1) = (I + A)x(n) + i=1 Bix(n - i), n = 0, 1, .. . is studied, where x = (x1 x2 ... xm)T is an unknown vector, m and s are fixed positive integers, A, Bi are square constant matrices and I is a unit matrix. A new degenerated Lyapunov-Krasovskii functional is used to derive sufficient conditions for exponential stability and to derive an exponential estimate of the norm of solutions. Though often used in the study of stability, the assumption that the spectral radius of the matrix of linear terms is less than 1 is not applied here. The criterion derived is illustrated by an example and compared with previously known results.

Keywords

Exponential stability; Lyapunov-Krasovskii functional; Degenerated functional; Multiple delays; Exponential estimate; Norm

Key words in English

Exponential stability; Lyapunov-Krasovskii functional; Degenerated functional; Multiple delays; Exponential estimate; Norm

Authors

DIBLÍK, J.

RIV year

2024

Released

01.08.2023

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Location

OXFORD

ISBN

1873-5452

Periodical

Applied Mathematics Letters

Volume

142

Number

108654

State

United States of America

Pages from

1

Pages to

6

Pages count

6

URL

https://www.sciencedirect.com/science/article/pii/S0893965923000861?via%3Dihub

BibTex

@article{BUT183778,
  author="Josef {Diblík}",
  title="Exponential stability of linear discrete systems with multiple delays by degenerated Lyapunov-Krasovskii functionals",
  journal="Applied Mathematics Letters",
  year="2023",
  volume="142",
  number="108654",
  pages="1--6",
  doi="10.1016/j.aml.2023.108654",
  issn="0893-9659",
  url="https://www.sciencedirect.com/science/article/pii/S0893965923000861?via%3Dihub"
}