A current-limiting droop controller is proposed\ud for single-phase grid-connected inverters with an\ud LCL filter that can operate under both normal and faulty\ud grid conditions. The controller introduces bounded nonlinear\ud dynamics and, by using nonlinear input-to-state stability\ud theory, the current-limiting property of the inverter is analytically\ud proven. The proposed controller can be operated\ud in the set mode to accurately send the desired power to the\ud grid or in the droop mode to take part in the grid regulation,\ud while maintaining the inverter current below a given\ud value at all times. Opposed to the existing current-limiting\ud approaches, the current limitation is achieved without external\ud limiters, additional switches or monitoring devices\ud and the controller remains a continuous-time system guaranteeing\ud system stability. Furthermore, this is achieved\ud independently from grid voltage and frequency variations,\ud maintaining the desired control performance under grid\ud faults as well. Extensive experimental results are presented\ud to verify the droop function of the proposed controller and\ud its current-limiting capability under normal and faulty grid\ud conditions.