Geodesic
Converse theorem for practical stability of nonlinear impulsive systems and applications
Kybernetika, Tome 54 (2018) no. 3, pp. 496-521 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.14736/kyb-2018-3-0496
Classification : 34A37, 34D20
Keywords: converse Lyapunov theorem; practical asymptotic stability; impulsive systems; cascade systems; perturbed systems 
@article{10_14736_kyb_2018_3_0496,
     author = {Ghanmi, Boulbaba and Dlala, Mohsen and Hammami, Mohamed Ali},
     title = {Converse theorem for practical stability of nonlinear impulsive systems and applications},
     journal = {Kybernetika},
     pages = {496--521},
     year = {2018},
     volume = {54},
     number = {3},
     doi = {10.14736/kyb-2018-3-0496},
     mrnumber = {3844829},
     zbl = {06987019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-3-0496/}
}
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
SP  - 496
EP  - 521
VL  - 54
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-3-0496/
DO  - 10.14736/kyb-2018-3-0496
LA  - en
ID  - 10_14736_kyb_2018_3_0496
ER  - 
%0 Journal Article
%A Ghanmi, Boulbaba
%A Dlala, Mohsen
%A Hammami, Mohamed Ali
%T Converse theorem for practical stability of nonlinear impulsive systems and applications
%J Kybernetika
%D 2018
%P 496-521
%V 54
%N 3
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-3-0496/
%R 10.14736/kyb-2018-3-0496
%G en
%F 10_14736_kyb_2018_3_0496
Ghanmi, Boulbaba; Dlala, Mohsen; Hammami, Mohamed Ali. Converse theorem for practical stability of nonlinear impulsive systems and applications. Kybernetika, Tome 54 (2018) no. 3, pp. 496-521. doi: 10.14736/kyb-2018-3-0496

Cité par Sources :