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Abstract

In this paper, we introduce the notion of h-stability for set-valued differential equations. Necessary and sufficient conditions are established by using Lyapunov theory. Then, based on the obtained results, we study the ℎ-stability of perturbed and cascaded systems. Finally, an example illustrates the proposed theorems
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Authors and Affiliations

Sihem Boukthir
1 2
ORCID: ORCID
Boulbaba Ghanmi
3
ORCID: ORCID
Imed Basdouri
3
ORCID: ORCID
Dalil Ichalal
4
ORCID: ORCID
Jean Lerbet
5

  1. Department of Mathematics, Faculty of Sciencesof Sfax, Route Soukra Km 4, BP 802, 3018, Sfax, Tunisia
  2. The IBISC laboratory, University ofEvry Val d’Essonne, University of Paris Saclay University, 40, rue de Pelvoux, 91020, Evry Courcouronnes,France
  3. Department of Mathematics, Faculty of Sciences of Gafsa, Sidi AhmedZarroug, 2112, Gafsa, Tunisia
  4. The IBISC laboratory, University of Evry Vald’Essonne, University of Paris Saclay University, 40, rue de Pelvoux, 91020, Evry Courcouronnes, France
  5. The LaMME laboratory, UMR CNRS 8071, Universityof Evry Val d’Essonne, University of Paris Saclay, 23 Bd de France, 91037, Evry CEDEX, France

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