Stabilization Control for Limit Cycle of an Inverted Pendulum System

In this paper, a kind of limit cycle of an inverted pendulum system is discussed. We propose a stabilization control law for such a limit cycle of an inverted pendulum system that the pendulum rotates periodically. Besides, the stabilization control law is extended so as to ensure not only stability of the limit cycle but also an L$_2$-gain disturbance attenuation in the presence of modeling error and viscosity friction.