A modified sequential shifting control algorithm is proposed for changing the helicopter rotor's speed in a large variation and providing continuous output power to the rotor. Two turbo-shaft engines and two multi-speed gearboxes, coordinating with the rotor, facilitate a wide rotor speed variation and provide continuous torque to the rotor. In the process of shifting, a new control scheme is proposed to design turbo-shaft engines' power turbine speed controller which is robust linear matrix inequality control, combined with active disturbance rejection control torque feed-forward compensation, so as to weaken engines' torque disturbance in rotor speed variation process. In the end, some numerical simulations are carried out to verify the feasibility of the shifting algorithm, based on the integrated helicopter/engine system model which can simulate auto-flight tasks of the real system. The simulation results show that the turbo-shaft engine's torque disturbance has little influence on engine power turbine speed in the process of torque shifting, and the rotor speed can perform large and rapid speed changes smoothly.