Abstract: In this paper, the problems of robust stability for linear time-varying uncertain periodic descriptor systems are treated. Based on the results of Lyapunov inequality of linear time-varying periodic descriptor systems, the definition of robust stability is put forward, and by using linear matrix inequalities, a necessary and sufficient condition is obtained for the systems to be robustly stable. Then, the condition that the close-loop system under state feedback control is robustly stable is considered and a kind of state feedback robust controllers is presented. Finally, the definition of quadratic stability is introduced, and the relation between quadratic stability and robust stability of the systems is discussed.