Asymptotic behaviors of solutions of a class of time-varying differential equations-Reference-Cited by-同舟云学术

Asymptotic behaviors of solutions of a class of time-varying differential equations

Published:2022-10-26 Issue:1 Volume:30 Page:95-109
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Hammi Mekki¹,Hammami Mohamed Ali²,Eddine Abbes Imad²

Affiliation:

1. IPEIG-Gafsa , University of Gafsa , Gafsa , Tunisia

2. Department of Mathematics , Faculty of Sciences of Sfax , University of Sfax , Sfax , Tunisia

Abstract

Abstract This paper deals with the problem of the global uniform stability of nonlinear time-varying systems in the presence of perturbations. The main novelty relies on the fact that the proposed approach for stability analysis allows for the computation of the bounds which characterize the asymptotic convergence of solutions to a small ball centered at the origin. Therefore, we generalize some results which have already be announced in the literature. Furthermore, we provide a numerical example to validate the effectiveness of our main result.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2022-2193/pdf

Reference28 articles.

1. A. Ben Abdallah, M. Dlala and M. A. Hammami, Exponential stability of perturbed nonlinear systems, Nonlinear Dyn. Syst. Theory 5 (2005), no. 4, 357–367.

2. A. Ben Abdallah, M. Dlala and M. A. Hammami, A new Lyapunov function for stability of time-varying nonlinear perturbed systems, Systems Control Lett. 56 (2007), no. 3, 179–187.

3. A. Benabdallah, I. Ellouze and M. A. Hammami, Practical stability of nonlinear time-varying cascade systems, J. Dyn. Control Syst. 15 (2009), no. 1, 45–62.

4. A. Benabdallah, I. Ellouze and M. A. Hammami, Practical exponential stability of perturbed triangular systems and a separation principle, Asian J. Control 13 (2011), no. 3, 445–448.

5. A. Benabdallah and M. A. Hammami, On the output feedback stability for non-linear uncertain control systems, Internat. J. Control 74 (2001), no. 6, 547–551.