Abstract
This paper studies the stability of time-delay systems with impulsive control involving stabilizing delays. A Razumikhin-type inequality with delayed impulses is proposed, where the information of time delay existing in impulses is effectively fetched and then integrated to the stabilization of time-delay systems. Some sufficient conditions ensuring global exponential stability (GES) for a class of nonlinear time-delay systems are obtained. The proposed conditions do not impose any restriction on the upper bounds of two consecutive impulse signals and on the size relation between time delays in system and in impulses, which is improved in the existing results on this topic. Moreover, our proposed results show that the time delays in impulses can contribute to the stability of the time-delay systems. Two numerical examples are given to demonstrate the applicability of our proposed results.
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