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Use of non-smooth impacts for the control of (otherwise) uncontrollable linear mechanical systems

A class of under actuated linear mechanical systems subject to nonsmooth impacts is considered, which would be uncontrollable if the impacts were absent. It is shown that just the nonsmooth impacts can be used in order to solve for the overall systems a dead-beat regulation problem, which would be impossible to be solved in absence of impacts due to the uncontrollability of the unconstrained mechanical system.