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For grid-connected inverters, switching harmonics can be effectively attenuated through an LCL-type filter. In order to suppress resonance and guarantee good performance, many strategies (e.g. active damping (AD), harmonic resonant control, repetitive control and grid feedforward) have been proposed. However, the wide variation of grid impedance value challenges system stability in practical applications. The aforementioned methods need to be investigated. This study evaluates the applicability of each part of the overall control in a weak grid case with the use of a stability criterion. It has been demonstrated that the feedback-based AD control can work well in a wide range of grid conditions. However, the resonant and repetitive control methods meet constraints. The grid feedforward method brings in an extra positive feedback path, and consequently results in high harmonics or even instability. Finally, a recommendation for system design has been presented. Simulations and experiments have been provided to verify the analysis.