The trajectory controllability of second order semi-linear systems using a functional analytic approach

This article examines the trajectory controllability (TC) of second-order evolution systems while taking impulses into account. A cosine family of operators produced by the linear component of the system, the integral version of Gronwall's inequality, and the idea of nonlinear functional analysis were used to describe the TC findings. Applications for finite- and infinite-dimensional systems of trajectory-controlled systems are given.