Stability of Switched Systems With Partial State Reset

In this note, we consider switched systems and switched systems with state reset. In particular we focus on the case of partial reset, i.e., where only some state components may undergo the action of a reset. First we consider switched systems with pre-specified (partial) reset and investigate under which conditions such systems are stable. In a second stage we consider the problem of stabilization by (partial) reset, which consists in finding a suitable (partial) reset for a given switched system that makes this system stable under arbitrary switching.