@Article{AAMM-15-1,
author = {Zhao, Guihua and Liang, Hui},
title = {Finite-Time Stability and Instability of Nonlinear Impulsive Systems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {1},
pages = {49--68},
abstract = {<p style="text-align: justify;">In this paper, the finite-time stability and instability are studied for nonlinear impulsive systems. There are mainly four concerns. 1) For the system with
stabilizing impulses, a Lyapunov theorem on global finite-time stability is presented.
2) When the system without impulsive effects is globally finite-time stable (GFTS) and
the settling time is continuous at the origin, it is proved that it is still GFTS over any
class of impulse sequences, if the mixed impulsive jumps satisfy some mild conditions.
3) For systems with destabilizing impulses, it is shown that to be finite-time stable, the
destabilizing impulses should not occur too frequently, otherwise, the origin of the
impulsive system is finite-time instable, which are formulated by average dwell time
(ADT) conditions respectively. 4) A theorem on finite-time instability is provided for
system with stabilizing impulses. For each GFTS theorem of impulsive systems considered in this paper, the upper boundedness of settling time is given, which depends
on the initial value and impulsive effects. Some numerical examples are given to illustrate the theoretical analysis.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0381},
url = {https://global-sci.com/article/72824/finite-time-stability-and-instability-of-nonlinear-impulsive-systems}
}