T-Controllability of Evolution Systems having Non-instantaneous Impulses

TL;DR

This paper investigates the controllability of evolution systems with non-instantaneous impulses, providing sufficient conditions using semigroup theory and Gronwall's inequality, validated through illustrative examples.

Contribution

It introduces new controllability conditions for non-instantaneous impulsive systems of integer order on Banach spaces, combining classical and nonlocal conditions.

Findings

Derived sufficient controllability conditions using semigroup properties.

Validated conditions with classical and nonlocal examples.

Enhanced understanding of impulsive system controllability.

Abstract

In this manuscript, we have considered the system governed by a noninstantaneous impulsive dynamical system of integer order with classical and nonlocal conditions and derived sufficient conditions for the trajectory controllability of the system on the Banach space. The conditions were obtained through the concept of semigroup properties of operator and Gronwall's inequality. Finally, illustrations with classical and nonlocal conditions were also added to validate the derived conditions.