Zeno Mode Control of Underactuated Mechanical Systems with Application to Pendubot Stabilization around the Upright Position

Switched control synthesis is developed for underactuated mechanical systems. In order to locally stabilize an underactuated system around an unstable equilibrium, its output is specified in such a way that the corresponding zero dynamics is locally asymptotically stable. Once such an output has been chosen, the desired stability property of the closed-loop system is provided by applying a Zeno mode controller, driving the system to the zero dynamics manifold in finite time. Although the present synthesis exhibits the Zeno behavior with an infinite number of switches on a finite time interval, it does not rely on the generation ofsliding modes, while providing robustness features similar to those possessed by their sliding mode counterparts. Theoretical results are supported by a simulation study made for a Pendubot.