Controllability for Volterra Integro-Dynamic Sylvester Matrix Systems with Impulse on Time Scales

This article presents the complete controllability for a Volterra integro-dynamic Sylvester matrix system with time scale impulses in a finite-dimensional space Rn. We utilized the Banach fixed point theorem and nonlinear functional analysis to determine the existence of a unique solution for the system, and conducted an analysis of complete controllability using the Gramian matrix and various parameter changes. We provided a numerical example using simulation to demonstrate the application of these conclusions for two different time scales, T=R and T=P_1,1.