On the vector Lyapunov functions and eventual stability of nonlinear impulsive differential equations - Ante, J.E.; Inyang, A.B.; Oduobuk, E.J.; Akai, U.P. (International Journal of Mathematical Analysis and Modelling, 2024)
In this paper, 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 functions. The novelty in the use of the vector form of the Lypunov function lies in the fact that the "restrictions" encountered via the use of scalar Lyapunov function is safely handled especially for large scale dynamical systems, since it involves splitting the Lyapunov functions into components so that each of the components can easily describe the behaviour of the solution state Together with comparison results, sufficient conditions for eventual stability are presented. Results obtained are extensions and improvements on existing results.