  We provide deterministic controllability conditions that imply exponential
mixing properties for randomly forced constrained dynamical systems with
possibly unbounded state space. As an application, new ergodicity results are
obtained for non-smooth models in elasto-plasticity driven by various types of
noise, including white noise. It is thereby illustrated how tools from control
theory can be utilized to tackle regularity issues that commonly arise in the
qualitative study of constrained systems.
