In this paper, a class of impulsive functional differential systems is investigated. It is proved that for the asymptotic stability of the zero solution of the system considered, it is sufficient that only some components of the right-hand side of the system are bounded for unbounded values of time. For functional differential equations without impulses, similar results were proved by Burton and Makay using Lyapunov–Krasovskii functionals. The goal of this paper is to prove these criteria for a class of impulsive functional differential systems with variable impulsive perturbations applying the Lyapunov–Razumikhin technique.
Digital Object Identifier (DOI)
J. Bohner, Martin and M. Stamova, Ivanka
"Asymptotic Stability Criteria for a Class of Impulsive Functional Differential Systems,"
Applied Mathematics & Information Sciences: Vol. 08
, Article 1.
Available at: https://dc.naturalspublishing.com/amis/vol08/iss4/1