In this paper, we consider switched systems that allow discontinuous
jumps in the state when switching occurs. In particular we analyze the
case where these jumps are dictated by a state reset rule. We show that
it is possible to study the state trajectories of a switched system with
state reset by means of some switched systems without state resets,
i.e., with continuous state trajectories. We establish some sufficient
conditions for stability of switched systems with state reset using the
associated systems without reset. The obtained results are used in
numerical examples to show the effectiveness of the proposed approach.