In this paper, reactive power sharing for Photovoltaic (PV) units in islanded microgrids has been formulated as a robust control design problem and is solved using convex optimization method. In addition to reactive power sharing, the disturbance rejection for voltage and active power have been formulated using infinity-norm constraints on the sensitivity functions and considered in the design. The proposed method uses only the measurement data of the power system with no need for a parametric model of the power grid equipment. The size of the problem is independent of the order of the plant which makes it applicable to power systems including a high number of buses and equipment such as synchronous generators, batteries and inverters. In the proposed method, the communication system can be considered in the control design process for centralized, distributed and decentralized structures. The proposed method has been validated through simulation of a microgrid encompassing synchronous generator, switching inverters and storage system. The results show that this method has successfully shared reactive power among different PV units while providing disturbance rejection for voltage and active power.