Microgrids (MG) are considered as a potential factor while focusing on a reliable supply and flexible control capabilities at the distribution side. These are broadly classified by two types, the grid supported or the grid connected and, the islanded or isolated type. Islanded types of microgrids are very sensitive towards voltage and frequency variations, therefore, a robust, as well as adaptive controller, always desired to control such variations within the microgrid. In this paper, a design perspective of a dc-dc boost converter is proposed, which stabilizes the output voltage variations with the help of a modification in the MIT rule. A set of inputs are considered and applied to the converter to validate the accuracy of the proposed model with the help of adaptation gain. The model reference adaptive controller is used to check the effect of adaptation gain on the output of dc-dc boost converter. An appropriate output voltage regulation and robust behavior pertaining to solar photovoltaic unregulated dc output voltage are exhibited. Design of A Model Reference Adaptive Controller (MRAC) for DC-DC Boost Converter for Variations in Solar Outputs using modified MIT Rule in an Islanded Microgrid