Sufficient conditions for uniform exponential stability and h-stability of some classes of dynamic equations on arbitrary time scales

Bacem Ben Nasser; Khaled Boukerrioua; Michael Defoort; Mohamed Djemai; Mohamed Ali Hammami; Taous Meriem Laleg-Kirati

doi:10.1016/j.nahs.2018.10.009

Sufficient conditions for uniform exponential stability and h-stability of some classes of dynamic equations on arbitrary time scales

Bacem Ben Nasser^*, Khaled Boukerrioua, Michael Defoort, Mohamed Djemai, Mohamed Ali Hammami, Taous Meriem Laleg-Kirati

^*Corresponding author for this work

Computer, Electrical and Mathematical Sciences and Engineering

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

26 Scopus citations

Abstract

This paper investigates the exponential stability and h-stability problems of some classes of nonlinear systems. First, we analyze the global uniform exponential stability for a class of integro-differential equations on time scales. We also derive some sufficient conditions for stability using an integral inequality approach. Then, we give an analysis of the h-stability of some classes of linear systems under Lipschitz-type disturbances. To this end, some h-stability criteria are established. Finally, numerical examples are proposed to illustrate the stability concepts.

Original language	English (US)
Pages (from-to)	54-64
Number of pages	11
Journal	Nonlinear Analysis: Hybrid Systems
Volume	32
DOIs	https://doi.org/10.1016/j.nahs.2018.10.009
State	Published - May 2019

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Ltd

Keywords

Dynamic equations on time scales
Exponential stability
Time scale integral inequalities
h-stability

ASJC Scopus subject areas

Control and Systems Engineering
Analysis
Computer Science Applications

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10.1016/j.nahs.2018.10.009

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title = "Sufficient conditions for uniform exponential stability and h-stability of some classes of dynamic equations on arbitrary time scales",

abstract = "This paper investigates the exponential stability and h-stability problems of some classes of nonlinear systems. First, we analyze the global uniform exponential stability for a class of integro-differential equations on time scales. We also derive some sufficient conditions for stability using an integral inequality approach. Then, we give an analysis of the h-stability of some classes of linear systems under Lipschitz-type disturbances. To this end, some h-stability criteria are established. Finally, numerical examples are proposed to illustrate the stability concepts.",

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AU - Ben Nasser, Bacem

AU - Boukerrioua, Khaled

AU - Defoort, Michael

AU - Djemai, Mohamed

AU - Hammami, Mohamed Ali

AU - Laleg-Kirati, Taous Meriem

PY - 2019/5

Y1 - 2019/5

N2 - This paper investigates the exponential stability and h-stability problems of some classes of nonlinear systems. First, we analyze the global uniform exponential stability for a class of integro-differential equations on time scales. We also derive some sufficient conditions for stability using an integral inequality approach. Then, we give an analysis of the h-stability of some classes of linear systems under Lipschitz-type disturbances. To this end, some h-stability criteria are established. Finally, numerical examples are proposed to illustrate the stability concepts.

AB - This paper investigates the exponential stability and h-stability problems of some classes of nonlinear systems. First, we analyze the global uniform exponential stability for a class of integro-differential equations on time scales. We also derive some sufficient conditions for stability using an integral inequality approach. Then, we give an analysis of the h-stability of some classes of linear systems under Lipschitz-type disturbances. To this end, some h-stability criteria are established. Finally, numerical examples are proposed to illustrate the stability concepts.

KW - Dynamic equations on time scales

KW - Exponential stability

KW - Time scale integral inequalities

KW - h-stability

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DO - 10.1016/j.nahs.2018.10.009

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SN - 1751-570X

VL - 32

SP - 54

EP - 64

JO - Nonlinear Analysis: Hybrid Systems

JF - Nonlinear Analysis: Hybrid Systems

ER -

Sufficient conditions for uniform exponential stability and h-stability of some classes of dynamic equations on arbitrary time scales

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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