Abstract: Considering a class of the time-varying periodically singular system, the concept of robust stability and robust stabilization for the time-varying periodically singular system was put forward by using analysis method of inequalities of linear matrix and Lyapunov inequalities. The necessary and sufficient conditions of robust fault-tolerant H_∞ control was obtained. The conclusion of robust fault-tolerant H_∞ control research achievements are the natural extension from time-invariant singular system to the timevarying periodically singular system. Finally, a numerical example is taken to illustrate the effectiveness of the obtained conclusions.