PI controllers are easy to use, adaptable and robust. Therefore, they are widely used in inverters with uncertain loads. However, H-bridge inverters are strong nonlinear systems and necessarily exhibit typical complex dynamic behavior. This paper takes PI-control H-bridge inverter as the research object. Firstly, the stroboscopic mapping theory is used to establish the discrete mathematical model of the inverter. Secondly, when the integral adjustment factor  is fixed, a bifurcation diagram with the proportional adjustment factor as the bifurcation parameter is obtained, and verified by iterative and time domain diagrams. When the proportional adjustment factor  is fixed, a bifurcation diagram with the integral adjustment factor as the bifurcation parameter is obtained, and verified by a stroboscopic graph and a spectrum graph. Thirdly, the stability of the system is analyzed by using the fast-changing stability theorem, which further verifies the consistency between simulation and theoretical analysis. Finally, research shows that external parameters such as input voltage , load inductance , and resistance   also have important effects on system stability. Therefore, this research has certain theoretical significance and practical engineering value for deep understanding the work stability of the H-bridge inverters system based on PI control and it can provide a strong theoretical guarantee for the design of this system.