H bridge inverter is a basic nonlinear topology in power electronic circuits. However it is prone to the generation of fast-scale instability phenomenon due to the variation of some parameters in the operation process, which can be eliminated with the slope compensation simply and effectively. Experience plays the leading role and common engineering design is lacking in necessary design criteria. Accrording to the bifurcation control theory of nonlinear system, in this paper we analyze the implementation of slope compensation on H bridge inverter under peak current mode control in detail, thereby obtaining the accurate amplitude requirements of the compensated slope signal and realize the optimization. The results of the analysis are consistent with those of simulation experiment, and the inverter circuit under appropriate slope compensation can operate in stable regime especially with the performances being enhanced remarkably. The research method is also applicable for the stability analysis of other power electronic circuits.