This paper presents the mathematical modeling for designing a 10[kW] DC-AC inverter system from 48 [V] DC to 120 V ACrms, considering its non-linear operation, allowing to obtain a detailed simulation to assess the proposed fuzzy PI control (with anti-windup action) and its optimal operation. The performance assessment of the converter was carried out with the discrete treatment of the voltage and current signals using spectral analysis, filtering considerations, and evaluation of limit cycle technique to determine the system's stability. The main results showed that THD at the filter output (transformer and capacitor) was around 0.0322% and 0.0632% at nominal load in open loop and closed loop, respectively. The inverter system presented more sensitivity in the current signal with a ripple at 120 [Hz] of 2.02% and at 5000 [Hz] of 10.62% (at nominal load). However, when the system operates in a closed loop, the current ripple at 120 [Hz] is 2.38% and at 5000 [Hz] is 10.62%.