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

- The finite time stability for nonlinear impulsive systems is investigated.
- Based on average impulse interval, less conservative sufficient condition for the finite time stability of nonlinear impulsive systems is obtained.
- Less conservative conditions for the sampling intervals of sampled-data systems to guarantee the finite time stability of linear sampled-data controlled systems is given. That is, when the AII of a sequence of impulsive signals ζ is equal to τα, the upper bound of the sampled intervals could be very large, while the lower bound of the sampled intervals could be also small enough.
- Two examples are given to show the effectiveness of the obtained results.

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.