For the high performance study of linear compressor with single mathematical model and control method, by analyzing the working principle of linear compressor, based on Lyapunov function, establish the mathematical model of low energy compressor system with frequency input and power output, compensate the uncertainty of the compressor, improve the transient performance, simulation and stability analysis.The compressor performance test bench was set up, and the fully automated multi-parameter test was realized based on Matlab software, obtaining the influence of parameter change on the performance of the compressor.The results show that when the working frequency is 54Hz , the refrigeration system enters the stable state for a shorter time and the power is lower; when the evaporation temperature is 30℃, the stability time is shorter and the power is lower; when the refrigerant is charged 300g, the stability time is shorter; the stable state and the consumption time is reduced by 32%, which proves that the proposed compressor system modeling method is feasible and efficient, and the proposed model control strategy has good low energy consumption and effectiveness.