  In this thesis, a non-penetrated and physically consistent non-smooth
numerical approach has been proposed, by employing the Prox formulation and
Moreau's mid-point time-stepping rule, for the contact dynamics with coupled
and decoupled constraints. Under this circumstance, the robust impulse-based
control has been successfully implemented and validated on the motion system of
controlled frictional oscillator. Further improvement has been achieved by
utilizing shooting method in the impulse estimating process instead of robust
estimation. This non-smooth numerical technique has been applied to the
under-actuated friction-coupled mulit-body system, by means of an
implementation on the controlled frictional Furuta pendulum. The specifically
designed impulse-based controller has successfully solved the problem of
stabilization of the inverted frictional Furuta pendulum, which is suffered
from the stiction effect of friction.
