Converse theorem for practical stability of nonlinear impulsive systems and applications

Boulbaba Ghanmi; Mohsen Dlala; Mohamed Ali Hammami

Kybernetika (2018)

  • Volume: 54, Issue: 3, page 496-521
  • ISSN: 0023-5954

Abstract

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The Lyapunov's second method is one of the most famous techniques for studying the stability properties of dynamic systems. This technique uses an auxiliary function, called Lyapunov function, which checks the stability properties of a specific system without the need to generate system solutions. An important question is about the reversibility or converse of Lyapunov's second method; i. e., given a specific stability property does there exist an appropriate Lyapunov function? The main result of this paper is a converse Lyapunov Theorem for practical asymptotic stable impulsive systems. Applying our converse Theorem, several criteria on practical asymptotic stability of the solution of perturbed impulsive systems and cascade impulsive systems are established. Finally, some examples are given to show the effectiveness of the derived results.

How to cite

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Ghanmi, Boulbaba, Dlala, Mohsen, and Hammami, Mohamed Ali. "Converse theorem for practical stability of nonlinear impulsive systems and applications." Kybernetika 54.3 (2018): 496-521. <http://eudml.org/doc/294864>.

@article{Ghanmi2018,
abstract = {The Lyapunov's second method is one of the most famous techniques for studying the stability properties of dynamic systems. This technique uses an auxiliary function, called Lyapunov function, which checks the stability properties of a specific system without the need to generate system solutions. An important question is about the reversibility or converse of Lyapunov's second method; i. e., given a specific stability property does there exist an appropriate Lyapunov function? The main result of this paper is a converse Lyapunov Theorem for practical asymptotic stable impulsive systems. Applying our converse Theorem, several criteria on practical asymptotic stability of the solution of perturbed impulsive systems and cascade impulsive systems are established. Finally, some examples are given to show the effectiveness of the derived results.},
author = {Ghanmi, Boulbaba, Dlala, Mohsen, Hammami, Mohamed Ali},
journal = {Kybernetika},
keywords = {converse Lyapunov theorem; practical asymptotic stability; impulsive systems; cascade systems; perturbed systems},
language = {eng},
number = {3},
pages = {496-521},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Converse theorem for practical stability of nonlinear impulsive systems and applications},
url = {http://eudml.org/doc/294864},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Ghanmi, Boulbaba
AU - Dlala, Mohsen
AU - Hammami, Mohamed Ali
TI - Converse theorem for practical stability of nonlinear impulsive systems and applications
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 3
SP - 496
EP - 521
AB - The Lyapunov's second method is one of the most famous techniques for studying the stability properties of dynamic systems. This technique uses an auxiliary function, called Lyapunov function, which checks the stability properties of a specific system without the need to generate system solutions. An important question is about the reversibility or converse of Lyapunov's second method; i. e., given a specific stability property does there exist an appropriate Lyapunov function? The main result of this paper is a converse Lyapunov Theorem for practical asymptotic stable impulsive systems. Applying our converse Theorem, several criteria on practical asymptotic stability of the solution of perturbed impulsive systems and cascade impulsive systems are established. Finally, some examples are given to show the effectiveness of the derived results.
LA - eng
KW - converse Lyapunov theorem; practical asymptotic stability; impulsive systems; cascade systems; perturbed systems
UR - http://eudml.org/doc/294864
ER -

References

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