The majority of common control methods focus on control parameter design based on discrete state variables obtained by digital sampling currently. In this study, the influence of sampling period on the stability of hybrid systems is studied by studying a double pendulum system controlled with digital proportional differential feedback. Firstly, through numerical simulation, it is found that the double pendulum nonlinear hybrid system can be qualitatively characterized by an approximate linearized system. The discrete mapping of state variables is then constructed to reveal the dynamic behavior of double pendulum hybrid system near the target position. Furthermore, a stability criterion of the double pendulum hybrid system is purposed. The criteria’s accuracy is verified with numerical simulation results.