Simple tests for uniform exponential stability of a linear delayed vector differential equation

Josef Diblik; Leonid Berezansky; Zdenek Svoboda; Zdenek Smarda

doi:10.1109/TAC.2021.3069901

Simple tests for uniform exponential stability of a linear delayed vector differential equation

Josef Diblik, Leonid Berezansky, Zdenek Svoboda, Zdenek Smarda

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A linear delayed vector equation is investigated. The system is considered in the most general setting and under weak assumptions on the entries of matrices of linear terms and delays. The main result on uniform exponential stability is universal in the sense that it generates a set of independent explicit statements (that can depend on all delays)on uniform exponential stability. The advantages over the existing results are demonstrated. The main tools employed by the paper include Bohl-Perron theorem, a priori estimates of solutions, and transformations of differential equations.

Original language	English
Journal	IEEE Transactions on Automatic Control
DOIs	https://doi.org/10.1109/TAC.2021.3069901
State	Accepted/In press - 1 Jan 2021

Keywords

Asymptotic stability
Bohl-Perron method
Control theory
Delay
Delays
Differential equations
Mathematical model
Mechanical variables measurement
Stability criteria
exponential stability
linear differential system
matrix measure
stability test

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.2021.3069901

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title = "Simple tests for uniform exponential stability of a linear delayed vector differential equation",

abstract = "A linear delayed vector equation is investigated. The system is considered in the most general setting and under weak assumptions on the entries of matrices of linear terms and delays. The main result on uniform exponential stability is universal in the sense that it generates a set of independent explicit statements (that can depend on all delays)on uniform exponential stability. The advantages over the existing results are demonstrated. The main tools employed by the paper include Bohl-Perron theorem, a priori estimates of solutions, and transformations of differential equations.",

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AU - Berezansky, Leonid

AU - Svoboda, Zdenek

AU - Smarda, Zdenek

N1 - Publisher Copyright: IEEE

PY - 2021/1/1

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N2 - A linear delayed vector equation is investigated. The system is considered in the most general setting and under weak assumptions on the entries of matrices of linear terms and delays. The main result on uniform exponential stability is universal in the sense that it generates a set of independent explicit statements (that can depend on all delays)on uniform exponential stability. The advantages over the existing results are demonstrated. The main tools employed by the paper include Bohl-Perron theorem, a priori estimates of solutions, and transformations of differential equations.

AB - A linear delayed vector equation is investigated. The system is considered in the most general setting and under weak assumptions on the entries of matrices of linear terms and delays. The main result on uniform exponential stability is universal in the sense that it generates a set of independent explicit statements (that can depend on all delays)on uniform exponential stability. The advantages over the existing results are demonstrated. The main tools employed by the paper include Bohl-Perron theorem, a priori estimates of solutions, and transformations of differential equations.

KW - Asymptotic stability

KW - Bohl-Perron method

KW - Control theory

KW - Delay

KW - Delays

KW - Differential equations

KW - Mathematical model

KW - Mechanical variables measurement

KW - Stability criteria

KW - exponential stability

KW - linear differential system

KW - matrix measure

KW - stability test

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JF - IEEE Transactions on Automatic Control

SN - 0018-9286

ER -

Simple tests for uniform exponential stability of a linear delayed vector differential equation

Abstract

Keywords

ASJC Scopus subject areas

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