This paper presents the small signal modelling and stability analysis of an inverter based microgrids with internal model control (IMC)-based robust droop controller. The robust droop control technique used for power sharing among the parallel operated inverters is without communication and is based on voltage and frequency droops respectively. An IMC based voltage and current controller is designed to maintain the system voltage and frequency within permissible limits. The dynamic equations of the microgrid system are developed and linearised around operating points. Subsequently, these equations are used to form a state space model of the considered microgrid system. The state space models of each inverter and its corresponding feedback controllers along with network and load are considered. Eigenvalue analysis is carried out to identify different frequency modes of the complete model and to determine the critical values of controller gains. The consequences of droop coefficients and gain on stability margins is studied in detail with the help of eigenvalue analysis. Further, this analysis and the effectiveness of the model is verified with time-domain simulation in MATLAB/SIMULINK. Results show that the IMC based robust droop controller improves the power-sharing and transient behaviour of the considered microgrid system.