Robust control of a DC microgrid under parametric uncertainty and disturbances

•A robust centralized controller is designed for an islanded DC microgrid.•The DGs of microgrid have parametric uncertainties and are exposed to input–output disturbances.•LMI approach is used to design the controller.•The proposed controller is robust against the disturbances and uncertainties. In this paper, a new robust centralized controller for a DC islanded microgrid is proposed. The proposed controller is designed to be robust against parametric uncertainties of the distributed generation units and to attenuate exogenous disturbances. In order to design the controller, a multi-input–multi-output, linear time-varying model of the DC microgrid is obtained. The upper and lower bounds of the uncertainties are determined by a Lebesque-measurable matrix, and a norm reduction criterion is applied for disturbance rejection. Moreover, it is assumed that all states of the system are measurable; thus, the state-feedback scheme is considered. The system stability is guaranteed by the Lyapunov theory. Linear matrix inequality constraints are formulated for the system and are solved for sub-optimal controller gains. The robustness of the proposed controller is verified via simulations, and the proposed control method is compared with existing schemes.