A novel approach to periodic event-triggered control: Design and application to the inverted pendulum.

In this paper, periodic event-triggered controllers are proposed for the rotary inverted pendulum. The control strategy is divided in two steps: swing-up and stabilization. In both cases, the system is sampled periodically but the control actions are only computed at certain instances of time (based on events), which are a subset of the sampling times. For the stabilization control, the asymptotic stability is guaranteed applying the Lyapunov-Razumikhin theorem for systems with delays. This result is applicable to general linear systems and not only to the inverted pendulum. For the swing-up control, a trigger function is provided from the derivative of the Lyapunov function for the swing-up control law. Experimental results show a significant improvement with respect to periodic control in the number of control actions.