CMMSE: An approach to the stability of Reset Switched Systems using a dynamics without reset

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.