This paper concerns time-delay systems with delayed impulses. "Average impulsive intervals" is used to replace the lower and upper bounds of impulsive intervals, which weakens the limitations to the impulsive sequences. Under some modified conditions on the impulsive functions and the Lyapunov-based function, the exponential stability of systems is established. A specific impulsive delayed system with linear input time-delays is investigated by virtue of the obtained results. Finally, some numerical example is given to demonstrate the applicability of our results.
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