The effect of delayed impulses on stability of impulsive time-delay systems

This paper investigates the problem of the effect of delayed impulses on stability of impulsive time-delay systems. Two types of delayed impulses are considered, that is, the destabilizing delayed impulses and the stabilizing delayed impulses. Under the assumption of bounded impulse input delays, Lyapunov-type sufficient conditions for stability of nonlinear time-delay systems are derived for each type of delayed impulses. Numerical results are presented to confirm the usefulness of the theoretical findings