  Rate-independent systems allow for solutions with jumps that need additional
modeling. Here we suggest a formulation that arises as limit of viscous
regularization of the solutions in the extended state space. Hence, our
parametrized metric solutions of a rate-independent system are absolutely
continuous mappings from a parameter interval into the extended state space.
Jumps appear as generalized gradient flows during which the time is constant.
The closely related notion of BV solutions is developed afterwards. Our
approach is based on the abstract theory of generalized gradient flows in
metric spaces, and comparison with other notions of solutions is given.
