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Instabilities due to mutual interactions among converters and inverters are sometimes observed. A system with multiple converters can be controlled stably overall when each converter is controlled according to each energy-based function like the Lyapunov function. This paper proposes a new Lyapunov-based digital control method. First its principle is derived especially for a digital control. Then a new numerical generator for reference waveforms is proposed to avoid complex analytical operations. It is applied to a grid-connected inverter with an LCL filter. The proposed methods are investigated and validated through simulation by Saber and experiment by a DSP-based digital control system.