Effects of impulse delays on Lp-stability of a class of nonlinear time-delay systems

Abstract

In this paper, a nonlinear time-delay system with delayed impulses and external disturbances is considered. The robustness problem of Lp-stability with respect to impulse-delays is addressed. In order to circumvent the technical difficulties caused by delayed impulses, the impulses-delayed system is modeled as an impulse-delay free system with switching impulses by means of an augmentation method. Based on the switching structure of the augmented system, a time-dependent Lyapunov function is constructed from the original Lyapunov function for the impulse-delay free case. Then by employing the new designed Lyapunov function combined with the use of Razumikhin-type arguments, sufficient conditions for exponential stability and Lp-stability are derived. The developed results characterize the relationship among the impulse intervals, the size of impulse-delays, and the level of Lp-gain. Two numerical examples are presented to illustrate the effectiveness of the developed methodology.