On the Global Existence of Solution of the Comparison System and Vector Lyapunov Asymptotic Eventual Stability for Nonlinear Impulsive Differential Systems.
Publication Date: 26/11/2024
Author(s): Jackson Efiong Ante, Ubong Dominic Akpan, Godwin Odido Igomah, Christian Solomon Akpan, Udeme Emmanuel Ebere, Peter Obeten Okoi, Samuel Okon Essang.
Volume/Issue: Volume 7 , Issue 4 (2024)
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.
