The existence and controllability of nonautonomous system influenced by impulses on both state and control

TL;DR

This paper investigates the controllability of nonautonomous impulsive integro-differential systems in Hilbert space, establishing existence of solutions and conditions for approximate controllability using fixed point methods and impulsive resolvent operators.

Contribution

It introduces new conditions for approximate controllability of impulsive nonautonomous systems in Hilbert spaces, utilizing impulsive resolvent operators and the adjoint problem.

Findings

Existence of mild solutions established via fixed point approach.

Derived conditions for approximate controllability.

Illustrative example demonstrating theoretical results.

Abstract

This paper examines impulsive controls related to nonautonomous impulsive integro-differential equations in Hilbert space, highlighting their significance. We establish the existence of the mild solution by using fixed point approach and present conditions for approximate controllability using impulsive resolvent operators and the adjoint problem, supported by an illustrative example.