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

22 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

Funding Information:
Research reported in this publication has been supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia . Also, this work has been supported by the European Community , the Regional Delegation for Research and Technology , the Haut de France Region, France and the National Center for Scientific Research, France under the projects ELSAT VUMOPE and the UVHC BI-CFNes.

Funding Information:
Research reported in this publication has been supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia. Also, this work has been supported by the European Community, the Regional Delegation for Research and Technology, the Haut de France Region, France and the National Center for Scientific Research, France under the projects ELSAT VUMOPE and the UVHC BI-CFNes.

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

Cite this

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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 - Boukerrioua, Khaled

AU - Defoort, Michael

AU - Djemai, Mohamed

AU - Hammami, Mohamed Ali

AU - Laleg-Kirati, Taous Meriem

N1 - Funding Information: Research reported in this publication has been supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia . Also, this work has been supported by the European Community , the Regional Delegation for Research and Technology , the Haut de France Region, France and the National Center for Scientific Research, France under the projects ELSAT VUMOPE and the UVHC BI-CFNes. Funding Information: Research reported in this publication has been supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia. Also, this work has been supported by the European Community, the Regional Delegation for Research and Technology, the Haut de France Region, France and the National Center for Scientific Research, France under the projects ELSAT VUMOPE and the UVHC BI-CFNes. Publisher Copyright: © 2018 Elsevier Ltd

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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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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

Access to Document

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