Everaldo M. Bonotto, Nivaldo G. Grulha Jr.
Abstract:
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.
Submitted September 8, 2009. Published June 8, 2010.
Math Subject Classifications: 34A37, 37B25, 54H20.
Key Words: Impulsive semidynamical systems; stability; Lyapunov functionals.
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| Everaldo M. Bonotto Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo-Campus de São Carlos Caixa Postal 668, 13560-970, São Carlos SP, Brazil email: ebonotto@icmc.usp.br |
Nivaldo G. Grulha Jr. Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo-Campus de São Carlos Caixa Postal 668, 13560-970, São Carlos SP, Brazil email: njunior@icmc.usp.br |
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