A Matrosov Theorem for Hybrid Systems With Memory

In this article, stability problems are investigated for hybrid systems with memory, which are developed to model hybrid systems affected by time delays. A nested Matrosov functional theorem is proposed to guarantee uniform asymptotic stability for time-varying hybrid systems with memory. Specifically, with a weak Lyapunov functional whose derivative in the flow set and whose difference in the jump set are negative semidefinite, if there exist some Matrosov functionals that satisfy nested conditions, uniform asymptotic stability can be asserted. The proposed result benefits from the concept of generalized solutions developed for hybrid systems with memory. Finally, an example is given to show the effectiveness of the result.