In this study, combined problem of robust output tracking and disturbance rejection for nonlinear semi-Markovian jump systems with time-varying delays and uncertainties is investigated in through improved-equivalent-input-disturbance-estimator (IEIDE)-based modified repetitive control (MRC) law. More precisely, IEIDE is introduced into the channel of control input to estimate and compensate the disturbance signals with high precision with an eye to attain the robust tracking performance. Subsequently, MRC block is internally embedded in the control loop that makes the system output signals to track the given reference signals inside the selected neighborhood of the equilibrium via repetitive learning. Furthermore, to obtain the controller and observer gain matrices , the linear matrix inequality conditions are derived based on the technique of Lyapunov stability . Finally, a switching boost converter circuit and single-link robot arm model are used to demonstrate the control scheme's efficiency and superiority. In addition to that the comparative study with the existing works are carried out. In this way, the potential benefits from practical perspectives of the developed results are validated.