Geodesic
Lyapunov stability of closed sets in impulsive semidynamical systems
Electronic journal of differential equations, Tome 2010 (2010)
In this article, we consider impulsive semidynamical systems, defined in a metric space, with impulse effects at variable times. Converse-type theorems are included in our results giving necessary and sufficient conditions for various types of stability of closed subsets of the metric space. These results are achieved by means of Lyapunov functionals which indicate how the solutions behave when entering a "stable" set.
Classification : 34A37, 37B25, 54H20
Keywords: impulsive semidynamical systems, stability, Lyapunov functionals 
@article{EJDE_2010__2010__a110,
     author = {Bonotto,  Everaldo M. and Grulha.,  Nivaldo G.jun.},
     title = {Lyapunov stability of closed sets in impulsive semidynamical systems},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1221.37026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a110/}
}
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Bonotto,  Everaldo M.; Grulha.,  Nivaldo G.jun. Lyapunov stability of closed sets in impulsive semidynamical systems. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a110/