A novel nonlinear current-limiting controller for three-phase grid-tied droop-controlled inverters that is capable of offering voltage support during balanced and unbalanced grid voltage drops is proposed in this paper. The proposed controller introduces a unified structure under both normal and abnormal grid conditions operating as a droop controller or following the recent fault-ride-through requirement to provide voltage support. In the case of unbalanced faults, the inverter can further inject or absorb the required negative sequence real and reactive power to eliminate the negative sequence voltage at the point of common coupling (PCC) whilst ensuring at all times boundedness for the grid current. To accomplish this task, a novel and easily implementable method for dividing the available current into the two sequences (positive and negative) is proposed, suitably adapting the proposed controller parameters. Furthermore, nonlinear input-to-state stability theory is used to guarantee that the total grid current remains limited below its given maximum value under both normal and abnormal grid conditions. Asymptotic stability for any equilibrium point of the closed-loop system in the bounded operating range is also analytically proven for first time using interconnected-systems stability analysis irrespective of the system parameters. The proposed control concept is verified using an OPAL-RT real-time digital simulation system for a three-phase inverter connected to the grid.