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

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

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10.1016/j.ifacol.2018.08.021

Cite this

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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.",

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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

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AU - Defoort, Michael

AU - Djemai, Mohamed

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PY - 2018/1/1

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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

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ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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