On the Global Existence of Solution of the Comparison System and Vector Lyapunov Asymptotic Eventual Stability for Nonlinear Impulsive Differential Systems.

Jackson Efiong Ante; Ubong Dominic Akpan; Godwin Odido Igomah; Christian Solomon Akpan; Udeme Emmanuel Ebere; Peter Obeten Okoi; Samuel Okon Essang

doi:10.52589/BJCNIT-ZDMTJB6G

On the Global Existence of Solution of the Comparison System and Vector Lyapunov Asymptotic Eventual Stability for Nonlinear Impulsive Differential Systems. | AB Journals

On the Global Existence of Solution of the Comparison System and Vector Lyapunov Asymptotic Eventual Stability for Nonlinear Impulsive Differential Systems.

;
;
;
;
;
;

British Journal of Computer, Networking and Information Technology

Vol. 7Issue 42024pp. 103–117Published 25 November 2024

DOI 10.52589/BJCNIT-ZDMTJB6G

Research Article

778Views

305Downloads

Metrics

Share Link

𝕏

Cite this

Citation unavailable for this article.

Abstract:

This paper examines the existence of maximal solution of the comparison system as well as the asymptotic eventual stability of nonlinear impulsive differential equations using the vector Lyapunov functions, which is generalized by a class of piecewise continuous Lyapunov functions. Together with comparison results, sufficient conditions for the asymptotic eventual stability of the impulsive systems. In the paper, it was established that the maximal solution of the comparison system majorizes the vector form of the Lyapunov functions. Together with comparison results, sufficient conditions for the asymptotic eventual stability of impulsive differential systems are presented . Results obtained improves and extends existing results in the literature.

Keywords:asymptotic eventual stability impulsive differential equation vector Lyapunov functions.

Copyrights

Authors retain copyright in their articles and have unrestricted rights to reuse, republish, archive, share, and distribute their work after publication.
All articles are published open access under the Creative Commons Attribution 4.0 International (CC BY 4.0) licence, which permits use, sharing, adaptation, distribution, and reproduction in any medium or format, including for commercial purposes, provided appropriate credit is given to the original author(s) and source.

Loading…

Disclaimer/Publisher’s Note

The statements, opinions and data contained in this publication are solely those of the author(s) and contributor(s) and not of AB Journals or its editors. AB Journals remains neutral and accepts no responsibility for any injury or damage resulting from ideas, methods, instructions or products referred to in the content.