Stability of Switched Systems With State Reset: Extending the Dynamic Reduction Approach

ABSTRACT This paper enhances the analysis of the stability of linear switched systems with state reset by extending a method, introduced in our previous work, that focuses on dynamic reduction without reset. We prove that if the boundedness condition is satisfied for both the norms of reset products and the inverses of reset matrices, then the stability of a switched system with state reset under arbitrary switching is equivalent to the stability of the corresponding time‐varying system obtained through dynamic reduction without reset. In cases where only the reset matrices satisfy the boundedness condition, we establish stability criteria using quadratic Lyapunov functions related to these reset matrices.