The robust stabilization of the cart pendulum system was studied under structured uncertainty with a continuous-time periodic controller. The cart pendulum system was considered here as the test set-up as it is a well-known example of an unstable nonminimum phase system. The uncertainty in the system rose due to measurement error or dry friction in it. In this paper, the robust stability of the periodic controller in the presence of uncertainty was examined. The gain margin and delay margin endow with the periodic controller were superior to those obtained in the case of linear time invariant (LTI) control even in the presence of such uncertainties.