Publication detail

# Exponential Stability of Linear Discrete Systems with Multiple Delays

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

Original Title

Exponential Stability of Linear Discrete Systems with Multiple Delays

English Title

Exponential Stability of Linear Discrete Systems with Multiple Delays

Type

journal article in Web of Science

Language

en

Original Abstract

The paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay $x\left( {k+1} \right)=Ax\left( k \right)+\sum_{i=1}^sB_ix\left( {k-m_i} \right)$, $k=0,1,\dots$ where $s\in \mathbb{N}$, $A$ and $B_i$ are square matrices and $m_i\in\mathbb{N}$. New criterion for exponential stability is proved by the Lyapunov method. An estimate of the norm of solutions is given as well and relations to the well-known results are discussed.

English abstract

The paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay $x\left( {k+1} \right)=Ax\left( k \right)+\sum_{i=1}^sB_ix\left( {k-m_i} \right)$, $k=0,1,\dots$ where $s\in \mathbb{N}$, $A$ and $B_i$ are square matrices and $m_i\in\mathbb{N}$. New criterion for exponential stability is proved by the Lyapunov method. An estimate of the norm of solutions is given as well and relations to the well-known results are discussed.

Keywords

exponential stability; exponential estimate; discrete system; Lyapunov method

Released

01.08.2018

Publisher

Hindawi

Location

Spojené Státy Americké

ISBN

1607-887X

Periodical

Discrete Dynamics in Nature and Society

Year of study

2018

Number

2018

State

US

Pages from

1

Pages to

7

Pages count

7

URL

Full text in the Digital Library

Documents

BibTex

```
@article{BUT149025,
author="Jaromír {Baštinec} and Hanna {Demchenko} and Josef {Diblík} and Denys {Khusainov}",
title="Exponential Stability of Linear Discrete Systems with Multiple Delays",
annote="The paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay $x\left( {k+1} \right)=Ax\left( k \right)+\sum_{i=1}^sB_ix\left( {k-m_i} \right)$,
$k=0,1,\dots$ where $s\in \mathbb{N}$, $A$ and $B_i$ are square matrices and $m_i\in\mathbb{N}$.
New criterion for exponential stability is proved by the Lyapunov method. An estimate of the norm of solutions is given
as well and relations to the well-known results are discussed.",
address="Hindawi",
chapter="149025",
doi="10.1155/2018/9703919",
howpublished="online",
institution="Hindawi",
number="2018",
volume="2018",
year="2018",
month="august",
pages="1--7",
publisher="Hindawi",
type="journal article in Web of Science"
}
```