  This paper studies input-to-state stability for hybrid systems with memory,
which models hybrid dynamics affected by time delays. Using both
Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals,
Lyapunov-based sufficient conditions are established for input-to-state
stability. In addition, further extensions and relaxations are proposed for
special cases, such as the stable flow/jump cases and the cases that Lyapunov
functions do not decrease strictly during flow/jumps. Finally, two examples are
used to illustrate the developed results.
