Razumikhin-type Theorems on Practical Stability of Dynamic Equations on Time Scales

Bacem Ben Nasser; Michael Defoort; Mohamed Djemai; Taous Meriem Laleg-Kirati

doi:10.1016/j.ifacol.2018.08.021

Razumikhin-type Theorems on Practical Stability of Dynamic Equations on Time Scales

Bacem Ben Nasser, Michael Defoort, Mohamed Djemai, Taous Meriem Laleg-Kirati

Computer, Electrical and Mathematical Sciences and Engineering

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

6 Scopus citations

Abstract

In this work, we investigate some Razumikhin-type criteria for the uniform global practical asymptotic stability on arbitrary time domains, for time-varying dynamic equations. Using Lyapunov-type functions on time scales, we develop appropriate inequalities ensuring that trajectories decay to the neighborhood of the trivial solution asymptotically. Some numerical examples are discussed to illustrate our results.

Original language	English (US)
Pages (from-to)	121-126
Number of pages	6
Journal	6th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2018: Oxford, United Kingdom, 11—13 July 2018
Volume	51
Issue number	16
DOIs	https://doi.org/10.1016/j.ifacol.2018.08.021
State	Published - Jan 1 2018

Bibliographical note

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

Publisher Copyright:
© 2018

Keywords

Dynamic equations on time scales
Lyapunov-Razumikhin techniques
Non-uniform time domains
Practical stability

ASJC Scopus subject areas

Control and Systems Engineering

Access to Document

10.1016/j.ifacol.2018.08.021

Cite this

@article{e151150164e64e308f4465e85283051c,

title = "Razumikhin-type Theorems on Practical Stability of Dynamic Equations on Time Scales",

abstract = "In this work, we investigate some Razumikhin-type criteria for the uniform global practical asymptotic stability on arbitrary time domains, for time-varying dynamic equations. Using Lyapunov-type functions on time scales, we develop appropriate inequalities ensuring that trajectories decay to the neighborhood of the trivial solution asymptotically. Some numerical examples are discussed to illustrate our results.",

keywords = "Dynamic equations on time scales, Lyapunov-Razumikhin techniques, Non-uniform time domains, Practical stability",

author = "{Ben Nasser}, Bacem and Michael Defoort and Mohamed Djemai and Laleg-Kirati, {Taous Meriem}",

note = "Funding Information: Research reported in this publication has been supported by the King Abdullah University of Science and Technology (KAUST). Also, this work has been supported by the European Community, the Regional Delegation for Research and Technology, the Haut de France Region and the National Center for Scientific Research under the projects ELSAT VUMOPE and the UVHC ∆I-CFNes. Publisher Copyright: {\textcopyright} 2018",

year = "2018",

month = jan,

day = "1",

doi = "10.1016/j.ifacol.2018.08.021",

language = "English (US)",

volume = "51",

pages = "121--126",

journal = "6th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2018: Oxford, United Kingdom, 11—13 July 2018",

issn = "2405-8963",

publisher = "Elsevier",

number = "16",

}

Razumikhin-type Theorems on Practical Stability of Dynamic Equations on Time Scales. / Ben Nasser, Bacem; Defoort, Michael; Djemai, Mohamed et al.
In: 6th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2018: Oxford, United Kingdom, 11—13 July 2018, Vol. 51, No. 16, 01.01.2018, p. 121-126.

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

TY - JOUR

T1 - Razumikhin-type Theorems on Practical Stability of Dynamic Equations on Time Scales

AU - Ben Nasser, Bacem

AU - Defoort, Michael

AU - Djemai, Mohamed

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). Also, this work has been supported by the European Community, the Regional Delegation for Research and Technology, the Haut de France Region and the National Center for Scientific Research under the projects ELSAT VUMOPE and the UVHC ∆I-CFNes. Publisher Copyright: © 2018

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this work, we investigate some Razumikhin-type criteria for the uniform global practical asymptotic stability on arbitrary time domains, for time-varying dynamic equations. Using Lyapunov-type functions on time scales, we develop appropriate inequalities ensuring that trajectories decay to the neighborhood of the trivial solution asymptotically. Some numerical examples are discussed to illustrate our results.

AB - In this work, we investigate some Razumikhin-type criteria for the uniform global practical asymptotic stability on arbitrary time domains, for time-varying dynamic equations. Using Lyapunov-type functions on time scales, we develop appropriate inequalities ensuring that trajectories decay to the neighborhood of the trivial solution asymptotically. Some numerical examples are discussed to illustrate our results.

KW - Dynamic equations on time scales

KW - Lyapunov-Razumikhin techniques

KW - Non-uniform time domains

KW - Practical stability

UR - http://www.scopus.com/inward/record.url?scp=85052642587&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2018.08.021

DO - 10.1016/j.ifacol.2018.08.021

M3 - Article

AN - SCOPUS:85052642587

SN - 2405-8963

VL - 51

SP - 121

EP - 126

JO - 6th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2018: Oxford, United Kingdom, 11—13 July 2018

JF - 6th IFAC Conference on Analysis and Design of Hybrid Systems ADHS 2018: Oxford, United Kingdom, 11—13 July 2018

IS - 16

ER -

Razumikhin-type Theorems on Practical Stability of Dynamic Equations on Time Scales

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this