In microgrid applications, stability issues have been raised into a matter of concern due to the continually increasing modern electronic loads and inverter-based power electronic loads. In this paper, adopting storage system based load side compensation technique, a Lyapunov redesign controller is proposed to considerably improve the microgrid stability in the presence of constant power loads. Besides the controller design, the robustness analysis of the proposed Lyapunov redesign controller against parameter uncertainties is depicted. After that, the proposed Lyapunov redesign controller robustness against parametric uncertainties, frequency variations, and additive white Gaussian noise (AWGN) is presented. Later, performance of the PID and Lyapunov redesign controller is compared in the case of nonlinearity, parameter uncertainties, and noise rejection to justify the selection of the Lyapunov redesign controller over the PID controller. Besides reckoning the necessary calculations, all of the results are verified in MATLAB/Simulink with the appreciable aftermath.