<p>The Andronov-Hopf Oscillator (AHO)-based inverter offers advantages such as low voltage harmonics and fast power response. However, it suffers from voltage fluctuations during load switching. To address this issue, this paper establishes the dynamic voltage model of the AHO inverter and analyzes the reasons for voltage fluctuations under load variations. By considering the nonlinear coupling between voltage amplitude and reactive power, along with the reactive power limits of the inverter, a high-gain robust voltage control strategy is proposed. The Global Uniform Ultimate Boundedness (GUUB) stability of the system is proved using Lyapunov's second method. Furthermore, the impact of control parameters on voltage characteristics is analyzed, and a particle swarm optimization (PSO)-based method is introduced for parameter selection. Additionally, a small-signal state-space model is developed to analyze the stability of the AHO inverter parallel system. Simulation results show that compared to the original AHO, the proposed control strategy can reduce the steady-state voltage deviation of the inverter by an average of 5.8% and the steady-state deviation of the bus voltage in the parallel system by an average of 2.9%. Compared to the proportional-integral (PI) voltage control strategy, the complexity of the proposed algorithm increases slightly. However, it can reduce the steady-state voltage deviation of the inverter by an average of 2.2% and exhibits better robustness in the parallel system. Meanwhile, the transient response time is improved. Hardware-in-the-loop (HIL) tests further demonstrate the effectiveness of the proposed strategy.</p>