Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system

This paper studies a specific mechanical example that is representative of a class of underactuated, weakly coupled, unstable mechanical systems that are exceptionally difficult to stabilize. In particular, systems in this class are not stabilizable using static smooth feedback but are stabilizable using nonsmooth feedback. Although similar purely theoretical developments have been previously presented, we emphasize the physical basis and physical implications of the theoretical conclusions in the context of a specific example. The development in this paper is limited to a specific physical example, but the approach is applicable to a wide class of underactuated, weakly coupled, unstable mechanical systems.