Publication detail

# STABILITY AND EXPONENTIAL STABILITY OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS AND SINGLE DELAY

DIBLÍK, J. KHUSAINOV, D. BAŠTINEC, J. SIRENKO, A.

Original Title

STABILITY AND EXPONENTIAL STABILITY OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS AND SINGLE DELAY

English Title

STABILITY AND EXPONENTIAL STABILITY OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS AND SINGLE DELAY

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 \begin{equation*} x\left( {k+1} \right)=Ax\left( k \right)+Bx\left( {k-m} \right), \quad k=0,1,\dots \end{equation*} where $A$, $B$ are square constant matrices and $m\in\mathbb{N}$. Sufficient conditions for exponential stability are derived using the method of Lyapunov functions and its efficiency is demonstrated by examples.

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 \begin{equation*} x\left( {k+1} \right)=Ax\left( k \right)+Bx\left( {k-m} \right), \quad k=0,1,\dots \end{equation*} where $A$, $B$ are square constant matrices and $m\in\mathbb{N}$. Sufficient conditions for exponential stability are derived using the method of Lyapunov functions and its efficiency is demonstrated by examples.

Keywords

Stability; Lyapunov function; delay; discrete system; matrix equation.

RIV year

2015

Released

08.08.2015

Publisher

Elsevier

ISBN

0096-3003

Periodical

APPLIED MATHEMATICS AND COMPUTATION

Year of study

269

Number

1

State

US

Pages from

9

Pages to

16

Pages count

8

URL

Documents

BibTex


@article{BUT116952,
author="Josef {Diblík} and Denys {Khusainov} and Jaromír {Baštinec} and Andrii {Sirenko}",
title="STABILITY AND EXPONENTIAL  STABILITY OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS AND SINGLE DELAY",
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
\begin{equation*}
x\left( {k+1} \right)=Ax\left( k \right)+Bx\left( {k-m} \right),
\end{equation*}
where $A$, $B$ are square constant matrices and $m\in\mathbb{N}$. Sufficient conditions for exponential stability
are derived using the method of Lyapunov functions and its efficiency is demonstrated by examples.",
}