This paper deals with a control strategy of multilevel converter topologies for integration of distributed generation (DG) resources into the power grid. The proposed control plan is based on the direct Lyapunov control (DLC) technique, which is an appropriate tool for the analysis and definition of a stable operating condition for DG link in the power grid. The compensation of instantaneous variations in the reference current components in ac side and dc voltage variations of cascaded capacitors in dc side of the interfacing system is considered properly, which is the main contribution and novelty of this paper in comparison with other control methods. By utilization of the proposed control technique, DG can provide continuous injection of active power in fundamental frequency from the dispersed energy sources to the grid. In addition, reactive power and harmonic current components of nonlinear loads can be provided with fast dynamic response, by setting a multiobjective reference current component in the current loop of DLC-based model. Therefore, achieving sinusoidal grid currents in phase with load voltages are possible, while the required power from the load side is more than the maximum capacity of interfaced multilevel converter. Simulation results confirm the effectiveness of the proposed control strategy in DG technology during dynamic and steady-state operating conditions