Abstract
This paper presents a new Lyapunov method for the input-to-state stability (ISS) of impulsive time-delay systems. The approach is proposed on the basis of an indefinite Lyapunov function rather than a negative definite one. When the continuous dynamics have a Lyapunov function with an indefinite time derivative, and the discrete dynamics are destabilizing, the impulsive system is ISS if an average dwell-time (ADT) condition is satisfying. A numerical example show their effectiveness and advantages.
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