Sufficient conditions for uniform exponential stability and h -stability of some classes of dynamic equations on arbitrary time scales

Bacem Ben Nasser (1, 2) , Khaled Boukerrioua (3) , Michael Defoort (4, 5) , Mohamed Djemai (4, 5) , Mohamed Ali Hammami (6) , Taous-Meriem Laleg-Kirati (1)

1 Computation a lBioscience Research Center (CBRC), Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE)
2 University of Kairouan
3 UBMA - Université Badji Mokhtar [Annaba]
4 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201
5 INSA Hauts-De-France - INSA Institut National des Sciences Appliquées Hauts-de-France
6 Université de Sfax - University of Sfax

This paper investigates the exponential stability and -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 -stability of some classes of linear systems under Lipschitz-type disturbances. To this end, some -stability criteria are established. Finally, numerical examples are proposed to illustrate the stability concepts.

Mots clés: Dynamic equations on time scales; Exponential stability; H-stability; Time scale integral inequalities

Domaines: Automatique / Robotique

Bacem Ben Nasser, Khaled Boukerrioua, Michael Defoort, Mohamed Djemai, Mohamed Ali Hammami, et al.. Sufficient conditions for uniform exponential stability and h -stability of some classes of dynamic equations on arbitrary time scales. Nonlinear Analysis: Hybrid Systems, 2019, 32, pp.54-64. ⟨10.1016/j.nahs.2018.10.009⟩. ⟨hal-03644208⟩