Exploiting discontinuities for stabilization of recurrent motions

A rigorous mathematical technique is presented for exploiting the presence of discontinuities in non-smooth dynamical systems in order to control the local stability of periodic or other recurrent motions. In particular, the formalism allows one to predict the effects of the control strategy based entirely on information about the uncontrolled system. The methodology is illustrated with examples from impacting systems, namely a model hopping robot and a Braille printer. It is shown how initially unstable motions can be successfully stabilized at negligible cost and without active energy injection.