In this paper, the stability of parallel-operated inverters in the sense of boundedness is investigated. At first, the non-linear model of parallelled inverters with a generic linear or non-linear load is obtained by using the generalised dissipative Hamiltonian structure and then the robust droop controller, recently proposed in the literature for parallel operation of inverters, is implemented in a way to produce a bounded control output. The proposed controller is called the bounded droop controller (BDC). It introduces a zero-gain property and can guarantee the boundedness of the closed-loop system solution. Therefore, for the first time, the closed-loop stability in the sense of boundedness is guaranteed for parallelled inverters feeding generic non-linear/linear loads. The controller structure is further improved to increase its robustness with respect to initial conditions, numerical errors or external disturbances while maintaining the stability property. Moreover, the controller is tuned to avoid any possible limit cycles in the voltage dynamics. Real-time simulation results for two single-phase inverters operated in parallel loaded with a non-linear load are presented to verify the effectiveness of the proposed BDC
