Abstract: According to the design problems of output feedback for general periodically tim-varying descriptor systems, by using the analysis methods of descriptor Lyapunov inequality and linear matrix inequality(LMI) and by introducing the feedback into the general periodically timevarying descriptor systems, an tribe controllers of output feedback was obtained for this kind of systems to be admissible and satisfy performance index of H_∞ control. The conclusions of output feedback research achievements are natural extend from descriptor systems to the general periodically timevarying descriptor systems. Finally, a numerical example was given to illustrate the effectiveness of the approach.