Several results on stability in impulsive dynamical systems are proved. The first main result gives equivalent conditions for stability of a compact set. In particular, a generalization of Ura's theorem to the case of impulsive systems is shown. The second main theorem says that under some additional assumptions every component of a stable set is stable. Also, several examples indicating possible complicated phenomena in impulsive systems are presented.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-1-9,
author = {Krzysztof Ciesielski},
title = {On Stability in Impulsive Dynamical Systems},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {52},
year = {2004},
pages = {81-91},
zbl = {1098.37017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-1-9}
}
Krzysztof Ciesielski. On Stability in Impulsive Dynamical Systems. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 81-91. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-1-9/