Compared with the Z source inverter, the circuit cost of the quasi switching boost inverter is greatly reduced. Therefore, it is more suitable for photovoltaic grid connected system. Research on grid-connected control for the quasi-switched boost inverter of photovoltaic system based on feedback linearization and μ-synthesis method is proposed when the uncertainty of the grid connected photovoltaic system is considered. Using feedback linearization method establishes the mathematical model of the inverter side. The controller K is designed by m-synthesis method. The method is simulated and verified. It has better dynamic performance when the external conditions are changed. And it can quickly restore the steady state and maintain a high power factor. When the parameter changes, it has less influence on the quality of grid connection. This work is supported by Natural Science Foundation of Shanghai (No. 13ZR1417800) and National Natural Science Foundation of China (No. 51405286), Shanghai Key Technologies R & D Program (No. 14110500700), and Key Laboratory for Substation Automatic Technique of Shanghai (No. 13DZ2273800).