Sufficient conditions for uniform exponential stability and h-stability of some classes of dynamic equations on arbitrary time scales. (May 2019)

• Record Type: Journal Article
• Authors: Ben Nasser, Bacem; Boukerrioua, Khaled; Defoort, Michael; Djemai, Mohamed; Hammami, Mohamed Ali; Laleg-Kirati, Taous-Meriem
• Is Part Of: Nonlinear analysis. Volume 32(2019)
• Page Start: 54
• Page End: 64
• Publication Date: 2019-05
• Subjects: Dynamic equations on time scales -- Exponential stability -- h-stability -- Time scale integral inequalities; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2018.10.009
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper investigates the exponential stability and h -stability problems of some classes of nonlinear systems. First, we analyze the global uniform exponential stability for a class of integro-differential equations on time scales. We also derive some sufficient conditions for stability using an integral inequality approach. Then, we give an analysis of the h -stability of some classes of linear systems under Lipschitz-type disturbances. To this end, some h -stability criteria are established. Finally, numerical examples are proposed to illustrate the stability concepts.