  Time-delayed control in a balancing problem may be a nonsmooth function for a
variety of reasons. In this paper we study a simple model of the control of an
inverted pendulum by either a connected movable cart or an applied torque for
which the control is turned off when the pendulum is located within certain
regions of phase space. Without applying a small angle approximation for
deviations about the vertical position, we see structurally stable periodic
orbits which may be attracting or repelling. Due to the nonsmooth nature of the
control, these periodic orbits are born in various discontinuity-induced
bifurcations. Also we show that a coincidence of switching events can produce
complicated periodic and aperiodic solutions.
