Aiming at the bifurcation and chaos of Buck-Boost matrix converter (BBMC) inverter stage under the action of pulse input voltage, a piecewise delay feedback control method is proposed to study the stability domain of its control parameters. The discrete iterative mathematical model of the inverter stage is established. The control characteristics of the inverter stage under the piecewise delay feedback control method are analyzed. The function relationship between the control parameters k1 and k2 during the stable operation of the system is determined. The stability domain range is determined. Finally, the correctness of the above theoretical analysis is verified by simulation. The results show that the piecewise delay feedback control can effectively suppress the chaotic phenomenon generated by the BBMC inverter stage under the pulse input voltage, which is of great significance for ensuring the stable operation of the BBMC inverter stage.