A periodic control system with hybrid inputs

It is of vital significance to stabilize and control a chaotic system. But, since the control system always has excessive fluctuations which make them always perform badly in the process of stabilization, a control model that makes the unstable system stable without excessive fluctuations is hereby developed. In the control model, one piecewise continuous control is added in each of the two halves of every control period. Then two impulses: one at the middle and another at the end of the control period of the system. Based on the Lyapunov's method, when the newly developed model is introduced into an appropriate chaotic system, it is proved to make the system stable. Precisely, the model can be applied to chaotic Chua's system and Lorenz system as examples to prove the validity of the results. Compared with other current control models, this model proves to control the unstable system more effectively in that it is more general and saves time.