In recent years, dc microgrid (MG) is increasing rapidly in electric power grids and other isolated systems, integrating more efficiency and suite better some of the renewable energy sources, storage units, and dc loads. However, dc MG stability analysis becomes a challenge when constant power loads (CPLs) are applied to dc bus, which introduces destabilizing effects in the system due to its negative impedance characteristics. This paper presents a novel robust controller, based on linear programming based on the Chebyshev theorem as a robust control technique considering the Kharitonov's theorem that ensures the minimization of the total deviation from the desired performance in a closed-loop system, specified by a family of characteristic polynomials. The purpose of the proposed controller is to tightly regulate the dc bus voltage, ensuring MG stability due to the effects of power variation on CPLs. The simulation and experimental tests are performed by using a MATLAB/Simulink simulator and a developed prototype of the DC MG system, respectively, to ratify the robustness and effectiveness of the proposed method of robust controller design.