Global Solution Existence and Eventual Stability for Nonlinear Systems with Impulses.
Publication Date: 11/07/2025
Author(s): Atsu J. U., Ante J. E., Ambrose U. U., Essang S. O., Aigberemhon E. M., Oyong S. B., Francis R. E..
Volume/Issue: Volume 8, Issue 2 (2025)
Page No: 129-140
Journal: African Journal of Mathematics and Statistics Studies (AJMSS)
Abstract:
In this paper, the existence of maximal solution of a comparison differential system for a class of piecewise continuous Lyapunov function is examined. Also, the eventual stability of nonlinear impulsive differential equations with fixed moments of impulse is examined using the vector Lyapunov functions, which is generalized by a class of piecewise continuous Lyapunov functions. The novelty in the use of the vector Lyapunov functions lies in the fact that the difficulty often encountered by the scalar Lyapunov function is allayed especially for large scale dynamical systems. Together with comparison results, sufficient conditions for eventual stability are presented.
Keywords:
Eventual stability; impulsive differential equation; Lyapunov functions.
