In recent years, DC microgrids supplying constant power loads (CPLs) have attracted significant attention due to their impact on overall system stability, which is attributed to their electrical characteristics that exhibit negative incremental impedance. This paper examines a secondary control strategy aimed at ensuring accurate power sharing and voltage restoration within an islanded DC microgrid supplying a constant power load. The droop control function is typically used in the primary control layer to facilitate power sharing among distributed generators (DGs). However, differing load profiles may cause the DC bus voltage to deviate from its nominal value. To restore the DC bus voltage to its nominal value while maintaining accurate power sharing, a primary and secondary control scheme is proposed. This scheme employs an integrated control strategy combining sliding mode control for the primary control level and H-infinity control for secondary control. The approach is based on a two-time-scale stability analysis, i.e., the settling time of the primary control must be faster than that of the secondary control. Additionally, compared to most existing methods, the proposed approach requires no global information and depends exclusively on DC bus voltage feedback, eliminating the need for passive loads in parallel with the CPL. A test system of an islanded DC microgrid feeding a CPL is created using Matlab and PSIM software to assess the proposed method. An experimental prototype comprising two DGs and a tightly voltage-controlled boost converter emulating a CPL is developed to demonstrate the proposed approach and confirm the theoretical results.