Three-phase inverters have many applications, including motor drive and grid converter systems. Grid connected inverters, as interface for renewable energy sources integration, are key elements of modern grids. While the inverter voltage and current regulation is performed using a digitally-controlled voltage source inverter (VSI), a control related delay is often not completely analysed in the control design. This results in an inaccurate inverter model and degraded performance. In this paper, a discrete-time inverter model with delayed control input is obtained. A linear-quadratic regulator (LQR) based current loop and integral control voltage loop are designed, achieving stable converter operation. Simulation results validate the effectiveness of the proposed model and controller design guideline for guaranteed stability. Experimental results demonstrate the applicability of the proposed model to a real-world scenario.