This is the research report concerned with the new stability concept and designing the controller of the time periodic systems. The periodic systems which is governed by time is very common in various type of dynamic systems. For example, the satellite is the large scale and the experimental test equipment as pendulum is also time periodic systems. The motion of the systems during the time interval is running repeatedly. While this periodic systems is running, the dynamic stability is important to behave the appropriate motion of the system's function. This research propose the new stability approach based on Lyapunov theorem which is analyzing the system's stability adapting the specific energy function. And also this research introduces the developing numerical procedures to retain the stability of time periodic system. Finally, the result of this research is very useful to judge the stability and design the controller of time periodic system.