Approximate controllability of impulsive differential equations with state-dependent delay

Abstract

In order to describe various real-world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process, impulsive differential equations have been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive differential equations with state-dependent delay is investigated. We study the approximate controllability for nonlinear impulsive differential system under the assumption that the corresponding linear control system is approximately controllable. Using methods of functional analysis and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.