Finite time stability of nonlinear impulsive systems and its applications in sampled-data systems

In this paper, we establish finite time stability (FTS) criteria for the nonlinear impulsive systems. By using a new concept called average impulse interval (AII), less conservative conditions are obtained for the FTS problem on the impulsive systems. Then we consider the linear time-invariant sampled-data systems by modeling such systems as linear impulsive systems. It is proved that when the AII of a sequence of impulsive signals ζ is equal to τα, the upper bound of the impulsive intervals could be very large, while the lower bound of the impulsive intervals could be also small enough. The obtained results are less conservative than the ones in the literature obtained for variable sampling intervals.