A note on the stability of linear time-delay systems with impulsive inputs

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 delayfree 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.