Consensus control is a decentralized method to balance reserved energy of multiple battery energy storage systems (BESSs) in a power network. It only requires each BESS unit to communicate with its neighboring units to share a few measurements. However, disturbance in data transmission may degrade the performance of consensus control and even undermine the system stability. The objective of this paper is to propose a droop-based consensus control method for a microgrid system with multiple BESS units and an extended Kalman filter (EKF) based dynamic state estimation (DSE) framework to withstand disturbances and measurement noise. Note that a distributed dynamic state estimator is employed for each individual BESS. To validate the performance of the control mechanism and DSE framework, MATLAB/SimPowerSystems is used to develop electromagnetic transient simulation testbeds for two microgrids with multiple BESS units in both grid-connected and islanded modes. The results verify that communication disturbances, including data loss, false data injection, communication interruption, along with measurement noise can be properly handled by the proposed approach.