  This paper studies impulsive stabilization of nonlinear systems. We propose
two types of event-triggering algorithms to update the impulsive control
signals with actuation delays. The first algorithm is based on continuous event
detection, while the second type makes decision about updating the impulsive
control inputs according to periodic event detection. Sufficient conditions are
derived to ensure asymptotic stability of the impulsive control systems with
the designed event-triggering algorithms. Lower bounds of the time period
between two consecutive events are also obtained, so that the closed-loop
impulsive systems are free of Zeno behavior. That is to say that the pulse
phenomena are excluded from the event-triggered impulsive control systems, in
the community of impulsive differential equations. An illustrative example
demonstrates effectiveness of the proposed algorithms and our theoretical
results.
