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),
\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.",
address="Elsevier",
chapter="116952",
doi="10.1016/j.amc.2015.07.037",
howpublished="print",
institution="Elsevier",
number="1",
volume="269",
year="2015",
month="august",
pages="9--16",
publisher="Elsevier",
type="journal article in Web of Science"
}