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This brief derives sufficiency-type stability results for time-delay linear systems with constant point delays under impulsive inputs of impulses of state-dependent amplitudes occurring separately through time. It is proved that the amplitudes of the impulses and the time intervals between impulses may be chosen sufficiently large if the delay-free dynamics is sufficiently stable compared to the delayed one. It is also seen that faster input impulses of appropriate amplitudes and signs may achieve stabilization if the delay-free dynamics is not exponentially stable.
Sen et al. (2003) studied this question.