Chaos control of chaotic pendulum system

We apply Lyapunov function method for designing a controller to control a pendulum system with chaotic motion to desired periodic motion such as period-one, period-two, period-four orbits. The controllability conditions are established based on the Lyapunov function method. Theoretical results are illustrated by numerical simulations which show the effect of control. A major advantage of this method is that the time consumption of control is shorter than the OGY method and SOGY method for the same parameters and initial point of the pendulum system.