Global Solution Existence and Eventual Stability for Nonlinear Systems with Impulses.

Atsu J. U.; Ante J. E.; Ambrose U. U.; Essang S. O.; Aigberemhon E. M.; Oyong S. B.; Francis R. E.

doi:10.52589/AJMSS-USLHJ4TC

Global Solution Existence and Eventual Stability for Nonlinear Systems with Impulses.

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African Journal of Mathematics and Statistics Studies

Vol. 8Issue 22025pp. 129–140Published 2 July 2025

DOI 10.52589/AJMSS-USLHJ4TC

Research Article

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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.

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